Fry faced strong criticism online for comparing costume designer Jenny Beavan to a "bag lady" when she picked up her Bafta for Mad Max.
Twitter users demanded Fry apologise for his comments over her clothes.
But Fry, a prolific Twitter user, said online afterwards Beavan was "a dear friend" who had "got" the joke.
The comedian and broadcaster underlined the point by posting a photo of the pair at the Bafta after-party.
He wrote: "Jenny Baglady Beavan and Stephen Outrageous Misogynist Swine Fry at the after party."
But on Monday morning, Fry appeared to have removed himself from the site.
Fry has been presenting the show for 11 years and audiences have become used to his cutting wit in the course of his role, often involving risque quips about many of the stars involved.
Beavan, who won the Bafta for Best Costume Design for Mad Max: Fury Road, came onto the stage at London's Royal Opera House wearing a black leather jacket, white t-shirt and dark trousers.
After her acceptance speech and she had left the stage, Fry said:  "Only one of the great cinematic costume designers would come to the awards dressed like a bag lady."
The joke however was not well-received and Twitter was soon alight with angry reaction and demands that Fry apologise.
Twitter user Wendy Evans was one of many others who felt Fry overstepped the mark when she wrote: "Stephen Fry's 'bag lady' comment was vile. Once again the achievement's of a female overshadowed by comments on her appearance."
But Fry hit back by first posting the photo of himself and Beavan at the party and then by angrily telling his critics they were "tragic people".
Nonetheless,  Fry also received support from others, including several celebrities.
Radio 1 Scott Mills DJ wrote: "I thought Stephen Fry was an excellent host tonight. Dealing with the biggest stars in the world is scary. I find this. He is a natural."
Comedian Matt Lucas joked: "Stephen Fry Didn't you get the memo? No-one is allowed to do jokes anymore."
British singer Adele - who has 25m followers - announced she was leaving Twitter in 2012 due to comments about her new-born son. She since returned, but revealed last year that she no longer sends her own messages due to "drunk tweeting".
Girls creator Lena Dunham said she was leaving Twitter last year to create a "safe space", after receiving online abuse for posting a picture on Instagram in a sports bra. Although her account is still active, it's believed to be run by a member of her creative team.
Actor and writer Matt Lucas left Twitter four years ago after a joke was tweeted about the death of his former civil partner, Kevin McGee. He has since rejoined the site.
US singer Chris Brown deleted his account in 2012 after receiving a barrage of tweets following a heated exchange with comedian Jenny Johnson. He was back on the site less than a week later.
In 2012, Kanye West quit the site by deleting all his tweets except for one announcing the release date of his Yeezus album and the words: "Be Back Soon." True to his word he was back, after a short break.
On Monday morning, following the sudden shutdown of Fry's Twitter account, calls to his agent were not answered.
The reasons for Fry leaving Twitter are not as clear as they may first appear as the comedian has shut his profile before - or threatened to do so.
In 2015,  he left the social media site in February until May without giving reasons.
He also pleaded for fans to stop sending him direct messages saying "it was impossible" for him to look at them if he wanted to have "anything close to a life."
In 2014,  Fry quit the site saying it was "unsafe" for him to tweet, adding he was filming "in a place whence I've been advised it is safest not to tweet".
And in 2009, he said he was going to leave after another user called his posts "boring".
Bafta show host Stephen Fry appears to have deleted his Twitter profile in the wake of his controversial comments during Sunday night's show.