The nephew of the late American President John F Kennedy had his account taken down after he "repeatedly shared debunked claims", a statement released by Facebook, which owns Instagram, said.
The 67-year-old's Facebook account remains active even though he has uploaded similar content to his page.
According to the BBC, one of his more troubling posts suggested the death of baseball player Hank Aaron, who died of natural causes last month aged 83, was linked to the Covid-19 vaccine.
Robert F Kennedy's representatives have been approached for comment.
Lawyer and environmentalist Kennedy is the son of the late senator, presidential candidate and former US attorney general, Robert F Kennedy.
He currently chairs the Children's Health Defense - a vaccine-sceptic group. In the past, he has campaigned against the immunisation of measles and was especially vocal during an outbreak of the disease.
Last year, he spoke at a conference for the National Vaccine Information Centre, a group which has been accused of spreading misinformation on vaccines.
He has previously addressed anti-lockdown protests and his videos are regularly used by similar-leaning activists based in other countries.
His niece, Kerry Kennedy Meltzer, is a physician. Last year, she wrote a piece in the New York Times entitled Vaccines are safe, no matter what Robert Kennedy Jr says.
Facebook has committed to removing false stories and claims about coronavirus vaccines to prevent "imminent physical harm".
