Posters have been put up warning colleagues not to eat them at work.
The ban was requested by a journalist who said she could suffer a fatal reaction if she came into contact with a banana, the Sun reported.
Workers at the BBC's new HQ in London decided to hang up posters of a banana with a giant cross through it.
It means staff are forbidden from unpeeling or consuming the fruit anywhere near others, the report said.
A BBC spokesman said: "The posters were put up for a colleague who has a strong medical sensitivity."
Banana allergies take two forms. The first is a reaction to tree pollen where victims experience itching and swelling in the mouth. With the more serious version people can suffer an anaphylactic reaction