The edict was issued three days after the gay journalist and former Tory MP Matthew Parris said on Newsnight that Mr Mandelson, the Secretary of State for Trade and Industry, was "certainly gay".
The ban was immediately criticised by Mo Mowlam, the Secretary of State for Northern Ireland, on BBC Radio 4's Any Questions on Friday evening.
Ms Mowlam said: "This is a serious error on the part of the BBC. It's insulting to us. We have our views but we are not about to be unfair to colleagues."
Accusing the corporation of acting with "grotesque incompetence", a senior BBC journalist said: "It's tosh, and has caused considerable irritation to journalists and editors. They resent being treated like children."
The ban, issued by Anne Sloman, the BBC's chief political adviser for editorial policy, stated: "Please will all programmes note that under no circumstances whatsoever should allegations about the private life of Peter Mandelson be repeated or referred to on any broadcast."
The senior BBC journalist said: "If Mandelson's sexuality were relevant then the idea the BBC should ignore it is a joke. Editors would resign rather than implement it."
Nine O'Clock News presenter Michael Buerk said: "If this decision was a result of some kind of political pressure it would be extremely worrying - but I don't think it's worked like that. The BBC is [just] anxious to do the right thing."Reuse content