In a blog post, the British actor, writer and comedian said he was deactivating his account because Twitter has become a "stagnant pool" littered with scum and other hazards.
"Even if you negotiate the sharp rocks you'll soon feel that too many people have peed in the pool for you to want to swim there any more. The fun is over," he wrote.
"Let us grieve at what twitter has become. A stalking ground for the sanctimoniously self-righteous who love to second-guess, to leap to conclusions and be offended -- worse, to be offended on behalf of others they do not even know."
Beavan accepted her BAFTA for costume design for "Mad Max: Fury Road" onstage at London's Royal Opera House while wearing slacks, a black leather jacket and a scarf over a white T-shirt.
After she finished her acceptance speech the BBC quoted Fry as saying
, "Only one of the great cinematic costume designers would come to the awards dressed like a bag lady."
Fry, who has appeared in "Sherlock Holmes: A Game of Shadows" and the "Hobbit" movies, is known for his provocative commentary. But Twitter immediately erupted in outrage.
Some users took it up as a feminist issue, saying no matter how successful a woman becomes she will still be criticized for her outfit. Others just felt as though the comment was rude.
Fry claimed that his comment was merely a joke between friends, one that Beavan did not mind. Before he quit Twitter, he posted a photo of the two of them embracing
after the awards ceremony.
"Yes we are friends, and I am absolutely not upset, but I don't want to talk any further because if I talk about it it will just create more fuss," the paper quoted her as saying.
And some people on Twitter came to Fry's defense, accusing a "self righteous" mob of overreacting.
Fry acknowledged that he will also be criticized for deactivating his Twitter account, but said he did not accept defeat.
"But you've let the trolls and nasties win! If everyone did what you did, Stephen, the slab-faced dictators of tone and humour would have the place to themselves," Fry wrote on his blog.
"Well, yes and they're welcome to it. Perhaps then they'll have nothing to smell but their own smell.
"So I don't feel anything today other than massive relief, like a boulder rolling off my chest. I am free, free at last."
Sunday night wasn't all bad for the BAFTA host, however. Viewers laughed as Fry imported an American sports-event tradition to the ceremony: the Kiss Cam.
"Talking of America, one of the wonderful things that great nation has given the world along with so many other things," Fry said. "The giant foam finger. Leaf blowers. Creationism. Syrup on bacon, but also the Kiss Cam."
As a heart-shaped camera focused on them and the audience cheered, Maggie Smith, 81, and Leonardo DiCaprio, 41, shared a sweet kiss on the cheek.