The interview is understood to have been prompted by a complaint from a woman who claimed she was raped in London in 1967.
Police said she was over the age of 18 at the time of the alleged incident.
Scotland Yard said a man in his seventies was interviewed under caution by appointment in London last month and that inquiries were continuing.
Lord Brittan, held the post of Home Secretary in Margaret Thatcher's Cabinet from 1983 to 1985 and later served as a European commissioner.
He said: "It is true that I have been questioned by the police about a serious allegation made against me. This allegation is wholly without foundation."