The announcement comes just hours after Twitter and Facebook temporarily locked Trump’s accounts after he addressed supporters who stormed the US Capitol.
The US president earlier posted a video to protesters urging them to go home, while also repeating claims of election fraud and telling them "we love you".
Twitter responded by locking his account for the first time and demanded he remove tweets excusing violence, while also threatening him with "permanent suspension" from the platform.
In a statement, Mr Zuckerberg said: "We believe the risks of allowing the President to continue to use our service during this period are simply too great,"
He added: "The shocking events of the last 24 hours clearly demonstrate that President Donald Trump intends to use his remaining time in office to undermine the peaceful and lawful transition of power to his elected successor, Joe Biden.
"His decision to use his platform to condone rather than condemn the actions of his supporters at the Capitol building has rightly disturbed people in the US and around the world.
"We removed these statements yesterday because we judged that their effect - and likely their intent - would be to provoke further violence."
ITV News International Affairs Editor Rageh Omaar on the international reaction to the scenes at the US Capitol on Wednesday:
Trump's ban on Facebook and Instagram comes just hours after he committed to an "orderly transition" of power to President-elect Joe Biden as the world reels from the scenes of chaos in the Capitol on Wednesday.
Watch ITV News Washington Correspondent Robert Moore's report from inside the US Capitol as protesters stormed the building
Despite rioting from Trump supporters, Congress worked through the night to approve the US election result.
Shortly after the result was announced, President Trump issue his statement but warned that "it’s only the beginning of our fight to Make America Great Again".
ITV News Washington Correspondent Robert Moore on what is next for Donald Trump:
Senators resumed business in Congress just hours after rioting Trump supporters stormed the Capitol.
Four people died, including a woman shot by police inside the building.
Three others died from "medical emergencies" and 52 people were arrested.
Home Secretary Priti Patel said Trump's statement in which he said "We love you" to the rioters and repeated his baseless claims of electoral fraud did "very little to de-escalate the situation".
"His comments directly led to the violence and so far he has failed to condemn that violence and that is completely wrong," Ms Patel said.
Inside the Washington siege - Robert Moore on his report that shocked the world