The US social media giant said Robinson, a controversial figure who founded the anti-Islam English Defence League (EDL), had used its platform to share "dehumanising language" and "calls for violence targeted at Muslims".
The company added it was closing his Facebook page and Instagram profile because its community standards forbid "hate speech that may create an environment of intimidation and exclusion for certain groups".
"Tommy Robinson's Facebook page has repeatedly broken these standards, posting material that uses dehumanising language and calls for violence targeted at Muslims," the company said in a statement.
"He has also behaved in ways that violate our policies around organised hate.
"This is not a decision we take lightly, but individuals and organisations that attack others on the basis of who they are have no place on Facebook or Instagram."
The social media firm is under pressure to rein in disinformation and the use of its platform to share hate speech and other malign material.
It follows a wave of scandals, mainly over the sharing of its users' data without their consent but also over the rampant use of its platform for Russian "fake news" influence campaigns during the 2016 US presidential elections.
A scathing British parliamentary report released last week branded Facebook "digital gangsters" who failed to fight the spread of fake news and violated data privacy.
Robinson, whose real name is Stephen Yaxley-Lennon -- the name of a well-known football hooligan from his hometown of Luton in central England that he has adopted -- is highly divisive in Britain.
He has prior convictions for drugs and assault and was also imprisoned last year for live-streaming outside a court in breach of reporting restrictions on a trial of a gang accused of sexual assault.
Robinson has a large following in the United States.
He defended himself in an interview with Britain's Press Association saying: "Where is free speech? I've breached no laws of Facebook... What I've done is shown people the truth, and that is what they are removing, the truth."
On Saturday he led a 4,000-strong protest against the BBC, which is preparing a documentary about him, outside its Manchester headquarters.
The US social media giant said Robinson, a controversial figure who founded the anti-Islam English Defence League (EDL), had used its platform to share "dehumanising language"