The nephew of late President John F Kennedy had his account permanently taken down “for repeatedly sharing debunked claims”, Facebook, which owns Instagram, said in a statement.
His Facebook account remains active despite similar claims posted there.
These have included linking the death of legendary baseball player Hank Aaron to the Covid-19 vaccine.
Facebook has vowed to remove false claims about Covid-19 vaccines to prevent “imminent physical harm”.
Mr Kennedy, a lawyer and environmentalist, is the son of late former US attorney general, senator and presidential candidate Robert F Kennedy.
Speaking last year at a conference for the National Vaccine Information Centre, a controversial group accused of spreading misinformation on vaccines, Mr Kennedy said people were hearing his message and “those seeds are landing on very fertile ground”.
He has addressed anti-lockdown protests and his videos are regularly translated by activists based in other countries.