Sidney Powell, a lawyer who was part of President Trump’s legal team, spread a conspiracy theory last month about election fraud. For days, she claimed that she would “release the Kraken” by showing voluminous evidence that Mr. Trump had won the election by a landslide.

But after her assertions were widely derided and failed to gain legal traction, Ms. Powell started talking about a new topic. On Dec. 4, she posted a link on Twitter with misinformation that said that the population would be split into the vaccinated and the unvaccinated and that “big government” could surveil those who were unvaccinated.

“NO WAY #America,” Ms. Powell wrote in the tweet, which collected 22,600 shares and 51,000 likes. “This is more authoritarian communist control imported straight from #China.” She then tagged Mr. Trump and the former national security adviser Michael T. Flynn — both of whom she had represented — and other prominent right-wing figures to highlight the post.

Ms. Powell’s changing tune was part of a broader shift in online misinformation. As Mr. Trump’s challenges to the election’s results have been knocked down and the Electoral College has affirmed President-elect Joseph R. Biden Jr.’s win, voter fraud misinformation has subsided. Instead, peddlers of online falsehoods are ramping up lies about the Covid-19 vaccines, which were administered to Americans for the first time this week.

Apart from Ms. Powell, others who have spread political misinformation such as Rep. Marjorie Taylor Greene, a Republican of Georgia, as well as far-right websites like ZeroHedge, have begun pushing false vaccine narratives, researchers said. Their efforts have been amplified by a robust network of anti-vaccination activists like Robert F. Kennedy Jr. on platforms including Facebook, YouTube and Twitter.

Among their misleading notions is the idea that the vaccines are delivered with a microchip or bar code to keep track of people, as well as a lie that the vaccines will hurt everyone’s health (the vaccines from Pfizer and Moderna have been proved to be more than 94 percent effective in trials, with minimal side effects). Falsehoods about Bill Gates, the Microsoft co-founder and philanthropist who supports vaccines, have also increased, with rumors that he is responsible for the coronavirus and that he stands to profit from a vaccine, according to data from media insights company Zignal Labs.

The shift shows how political misinformation purveyors are hopping from topic to topic to maintain attention and influence, said Melissa Ryan, chief executive of Card Strategies, a consulting firm that researches disinformation.

It is “an easy pivot,” she said. “Disinformation about vaccines and the pandemic have long been staples of the pro-Trump disinformation playbook.”

The change has been particularly evident over the last six weeks. Election misinformation peaked on Nov. 4 at 375,000 mentions across cable television, social media, print and online news outlets, according to an analysis by Zignal. By Dec. 3, that had fallen to 60,000 mentions. But coronavirus misinformation steadily increased over that period, rising to 46,100 mentions on Dec. 3, from 17,900 mentions on Nov. 8.

NewsGuard, a start-up that fights false stories, said that of the 145 websites in its Election Misinformation Tracking Center, a database of sites that publish false election information, 60 percent of them have also published misinformation about the coronavirus pandemic. That includes right-wing outlets such as Breitbart, Newsmax and One America News Network, which distributed inaccurate articles about the election and are now also running misleading articles about the vaccines.

John Gregory, the deputy health editor for NewsGuard, said the shift was not to be taken lightly because false information about vaccines leads to real-world harm. In Britain in the early 2000s, he said, a baseless link between the measles vaccine and autism spooked people into not taking that vaccine. That led to deaths and serious permanent injuries, he said.

“Misinformation creates fear and uncertainty around the vaccine and can reduce the number of people willing to take it,” said Carl Bergstrom, a University of Washington evolutionary biologist who has been tracking the pandemic.

Dr. Shira Doron, an epidemiologist at Tufts Medical Center, said the consequences of people not taking the Covid-19 vaccines because of misinformation would be catastrophic. The vaccines are “the key piece to ending the pandemic,” she said. “We are not getting there any other way.”

Ms. Powell did not respond to a request for comment.

To deal with vaccine misinformation, Facebook, Twitter, YouTube and other social media sites have expanded their policies to fact-check and demote such posts. Facebook and YouTube said they would remove false claims about the vaccines, while Twitter said it pointed people to credible public health sources.

The flow of vaccine falsehoods began rising in recent weeks as it became clear that the coronavirus vaccines would soon be approved and available. Misinformation spreaders glommed onto interviews by health experts and began twisting them.

On Dec. 3, for example, Dr. Kelly Moore, the associate director for immunization education at the nonprofit Immunization Action Coalition, said in an interview with CNN that when people receive the vaccine, “everyone will be issued a written card” that would “tell them what vaccine they had and when their next dose is due.”

Dr. Moore was referring to a standard appointment reminder card that could also be used as a backup vaccine record. But skeptics quickly started saying online that the card was evidence that the U.S. government intended to surveil the population and limit the activities of people who were unvaccinated.

That unfounded idea was further fueled by people like Ms. Powell and her Dec. 4 tweet. Her post pushed the narrative to 47,025 misinformation mentions that week, according to Zignal, making it the No. 1 vaccine misinformation story at the time.

To give more credence to the idea, Ms. Powell also appended a link to an article from ZeroHedge, which claimed that immunity cards would “enable CDC to track Covid-19 vaxx status in database.” On Facebook, that article was liked and commented on 24,600 times, according to data from CrowdTangle, a Facebook-owned social media analytics tool. It also reached up to one million people.

ZeroHedge did not respond to a request for comment.

In an interview, Dr. Moore said she could not believe how her words had been distorted to seem as if she was supporting surveillance and restrictions on unvaccinated members of the public. “In fact, I was simply describing an ordinary appointment reminder card,” she said. “This is an old-school practice that goes on around the world.”

Other supporters of Mr. Trump who said the election had been stolen from him also began posting vaccine falsehoods. One was Angela Stanton-King, a former Republican candidate for Congress from Georgia and a former reality TV star. On Dec. 5, she tweeted that her father would be forced to take the coronavirus vaccine, even though in reality the government has not made it mandatory.

“My 78 yr old father tested positive for COVID before Thanksgiving he was told to go home and quarantine with no prescribed medication,” Ms. Stanton-King wrote in her tweet, which was liked and shared 13,200 times. “He had zero symptoms and is perfectly fine. Help me understand why we need a mandatory vaccine for a virus that heals itself…”

Ms. Stanton-King declined to comment.

Anti-vaccination activists have also jumped in. When two people in Britain had an adverse reaction to Pfizer’s Covid-19 vaccine this month, Mr. Kennedy, a son of former Senator Robert F. Kennedy who campaigns against vaccines as chairman of the anti-vaccination group Children’s Health Defense, pushed the unproven notion on Facebook that ingredients in the vaccine led to the reactions. He stripped out context that such reactions are usually very rare and it is not yet known whether the vaccines caused them.

His Facebook post was shared 556 times and reached nearly a million people, according to CrowdTangle data. In an email, Mr. Kennedy said the Food and Drug Administration should “require pre-screening” of vaccine recipients and “monitor allergic and autoimmune reactions,” without acknowledging that regulators have already said they would do so.

Ms. Ryan, the disinformation researcher, said that as long as there were loopholes for misinformation to stay up on social media platforms, purveyors would continue pushing falsehoods about the news topic of the day. It could be QAnon today, the election tomorrow, Covid-19 vaccines after that, she said.

“They need to stay relevant,” she said. “Without Trump, they’re going to need new hobbies.”