In a letter to Anne Sloman, the BBC's chief political adviser, Mr Dimbleby has accused the BBC of "impertinence and ineptitude". He has copied the letter to senior news broadcasters.
His brother, David Dimbleby, is also believed to have written a separate letter of complaint to BBC executives.
Jonathan Dimbleby is understood to be especially angry that guests on his Radio 4 programme, Any Questions, were warned last Friday not to discuss the Trade and Industry Secretary's private life.
Mr Mandelson was "outed" as a homosexual by the columnist and former Tory MP Matthew Parris on the Newsnight programme last week.
The BBC issued a statement last night saying it had received Mr Dimbleby's letter and had "had amicable conversations" with him over the decision.
However, the corporation's position was becoming increasingly ridiculous as it emerged that news programmes can now discuss the furore surrounding the ban, but are still not allowed to mention what has been banned.Reuse content