Kennedy, the nephew of former US President John F. Kennedy, and his representatives could not be reached for a comment.
A lawyer and environmentalist, he is the son of the former US senator, attorney general and presidential candidate Robert F. Kennedy.
Facebook had earlier this week said it would expand a list of false health claims it bans from the platform to include debunked claims about vaccines, such as they are toxic or cause autism.
The Wall Street Journal had reported the news earlier in the day.