Facebook, meanwhile, added a fact check to an identical message posted to its platform, but did not go further.
Facebook has told readers that votes are still being counted and that the winner of the US presidential election has not been announced.
Facebook said it had activated a feature to place notifications at the top of the timelines for all US users, explaining that the election had not yet been decided.
"Once President Trump began making premature claims of victory, we started running notifications on Facebook and Instagram that votes are still being counted and a winner is not projected", it said.
Twitter said it had labelled Trump's tweet about the election being "stolen" because it violated the firm's civic integrity policy.
But the network appears to be allowing some claims of victory, despite warning that it would not.
An earlier tweet from Trump that he had enjoyed "a big win!" has been left untouched, as has a carefully-worded tweet from Biden that said "we believe we are on track to win this election".
No tweets from Mr Biden from election night have been labelled.
The Trump campaign has claimed that "Silicon Valley continues its campaign to censor and silence the president".