Health and Social Care Secretary Matt Hancock wants new legislation to force social media companies to remove content promoting false information about vaccines.
He said the government is working with internet companies to identify misleading material on jabs, including Measles, Mumps and Rubella (MMR).
Artificial intelligence programmes could root out bad science.
MMR vaccine uptake rates are declining in many countries.
The reason is not clear. Rates dipped in the 1990s following publication of a report linking MMR to autism, but partly recovered after that research was discredited and disproved.
However, the volume of anti-vaccine sentiment on social media has been swelling in recent years, sparking concern that it is having a negative impact.
Mr Hancock told the BBC's Today programme: "We are looking at legislating for the duty of care that social media companies in particular have towards the people on their sites - this is an important part of that duty of care alongside all the other things that social media companies need to do, like tackling material that promotes suicide and self-harm and, of course, terrorism."
In a statement Facebook, which owns Instagram, said: "We are working to tackle vaccine misinformation…by reducing its distribution and providing people with authoritative information on the topic."
Measures to be taken, according to the company, include rejecting ads with misinformation about vaccines and not showing misleading content on hashtag pages.
Serious health complications
Measles is highly infectious and can cause serious health complications, including damaging the lungs and brain.
There have been measles outbreaks in parts of the US. Rockland County in New York State has declared a State of Emergency in response to the outbreak there. Anyone who is under 18 and unvaccinated will be barred from all public places until the declaration expires in 30 days or they get the MMR vaccine. Breaches of the order will result in a fine and a six month jail sentence. In January officials in Washington State announced measures to help local areas worst affected by the virus.
There were more than 82,500 cases in Europe in 2018 - the highest number in a decade and three times the total reported in 2017.
Health chiefs in Greater Manchester reported a sharp increase in measles cases between January and March 2019, the majority in unvaccinated children.
In England, the proportion of children receiving both doses of the MMR jab by their fifth birthday has fallen over the last four years to 87.2%.
This is below the 95% said to provide "herd immunity", the level considered by experts to protect a population from a disease.
Prof Dame Sally Davies, England's chief medical officer, believes anti-vaccination campaigns are damaging and should be vigorously resisted: "I don't like it that bad science is pushed to parents - I don't like quackery - I want them to know the truth that vaccines are very safe that have been used for decades".
Jo Walton was sceptical about vaccinations when her daughter Sarah was due to receive her first jab. But Sarah contracted measles before the date of the injection.
The family thought no more of it until Sarah was 24 and was diagnosed with a degenerative neurological condition directly linked to the earlier measles infection.
Sarah is now bedbound and needs 24-hour care. Jo has become a committed campaigner for the MMR jab: "It upsets me greatly that here we are 14 years after Sarah's diagnosis and people seem as ill-educated about the consequences of childhood illnesses as I was back in 1980."
But, faced with a barrage of claims and counter-claims on social media, its not surprising that some parents are confused.
The question is whether health experts should try to win them over by striving to win that battle rather than setting out to remove material deemed to be damaging and inaccurate.
Winning heart and minds
Dr Fiona Godlee, editor of the British Medical Journal, argues that there is a danger with what may be perceived as censorship and, she says, the focus should be on winning hearts and minds.
"What you have is a spectrum of people, some for whom its an obvious thing to get their child vaccinated, others at the other end who will never be convinced, and, in the middle, perfectly intelligent, sensible people who are not certain what do and its that group of people we need to treat with respect and provide them with information.
"Social media can be both a positive and a negative thing in that. Clumsy-handed censorship I don't think is the way forward," she said.
As the chief medical officer put it, the UK's health system is not an island when it comes to the spread of viruses.
Social media and infectious diseases are global phenomena.
No wonder the World Health Organisation has declared the anti-vaccine movement to be one of the top global health threats for 2019.