The broadcaster read a direct quote from Andrew Rawnsley's book on the inner workings of New Labour - The End of the Party - which said: "(Gordon) Brown went berserk with Bob Shrum. 'How could you do this to me, Bob?' Brown screamed at a shaking Shrum. 'How could you fucking do this to me?'"
A few minutes later Paxman apologised to viewers for his use of the word.
He said: "Apparently I'm told by our editor I have to apologise for quoting what you said the Prime Minister said and using the f word there. So honour satisfied now."
A BBC spokesman said: "During a post watershed interview with Andrew Rawnsley, Jeremy read a direct quote from his book which contained an expletive. He apologised immediately to anyone that may have found it offensive."