Mr Fry said "only one of the great cinematic costume designers would come to an awards ceremony dressed as a bag lady" after Ms Beavan won the award for her work in Mad Max: Fury Road.
This is how Twitter reacted:
#stephenfry major fan of Stephen but reallty ' Bag Lady' comment unbecoming of somenone who has admitted to issues with the way they look!— Sue L (@brambs) February 14, 2016
Mr Fry, 58, who has presented the awards since 2001, responded on Twitter to those who were offended.
The comedian then proceeded to retweet comments that supported the joke and his humour, and responded personally to those who mentioned him in tweets. (Also Read: BAFTA 2016: Kate Winslet Was Asked to 'Settle For Fat Girl' Roles)
So just a word to the tragic figures who think calling Jenny Bevan a bag lady was an insult. She's a dear friend and she got it. Derrr— Stephen Fry (@stephenfry) February 14, 2016
The comedian worked with Ms Beavan on both Gosford Park and Sherlock Holmes: Game of Shadows.