The slur was shouted by a member of the audience who reportedly had Tourette syndrome as Sinners actors Delroy Lindo and Michael B Jordan presented the award for special visual effects on Sunday at London's Royal Festival Hall.
"Some viewers may have heard strong and offensive language during the BAFTA Film Awards 2026," a BBC spokesperson said.
"This arose from involuntary verbal tics associated with Tourette syndrome, and was not intentional.
"We apologise for any offence caused by the language heard."
The slur can still be heard on BBC iPlayer at the time of writing.
During the broadcast, the awards ceremony's presenter Alan Cumming issued an apology for the language viewers might hear.
"You may have heard some strong and offensive language tonight," he said.
"If you have seen the film I Swear, you will know that film is about the experience of a person with Tourette syndrome.
"Tourette syndrome is a disability and the tics you have heard tonight are involuntary, which means the person who has Tourette syndrome has no control over their language.
"We apologise if you were offended."
I Swear stars Robert Aramayo, and tells the story of Scottish campaigner for Tourette syndrome, John Davidson, who developed the condition when he was 12, and was in the audience for at least part of the ceremony.
Aramayo won best actor and the EE Rising Star for his performance in the film, which also won best casting.
The ceremony saw Sinners director Ryan Coogler become the first Black winner of the BAFTA for best original screenplay for the film, which also won best supporting actress for Wunmi Mosaku and original score.
The British Academy of Film and Television Arts, Tourette Scotland, Lindo and Jordan have been contacted for comment.
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