In the three-second scene two strangers have a passionate embrace in a library.
The head of the film board Ezekiel Mutua said Coca-Cola has agreed to release a new version of the commercial without the scene on Wednesday night.
KFCB previously asked YouTube to remove a music video about same-sex relationships on “moral grounds”.
Six adverts with the tagline “Taste the Feeling” were released globally in January, reports Ad Week.
The film board warned advertisers to consider if children would be watching at the time the advert is aired, reports the BBC’s Abdinoor Aden in the capital Nairobi.
Last month, the board complained about a sex party which they claimed was being used by an international pornography ring to make films.
In 2014 the film board banned the US film The Wolf of Wall Street because of “extreme scenes of nudity, sex, debauchery, hedonism and cursing”.