The head of the Muslim Council of Britain, Sir Iqbal Sacranie, is being investigated by police for saying that homosexuality was "harmful".
Sir Iqbal Sacranie also criticised civil partnerships
In an interview with BBC Radio 4's PM Programme on 3 January, Sir Iqbal also criticised same-sex civil partnerships.
However, he went on to say that everyone in society should be tolerant.
The Met Police said they were examining if his remarks constituted an offence under the Public Order Act, following a complaint from a member of the public.
Scotland Yard said in a statement that it had "received a report of comments made in a radio interview which the complainant believed were homophobic in nature and asked us to investigate".
The complaint was made on a police internet website.
In the interview Sir Iqbal said he was guided by the teachings of the Muslim faith, adding that other religions such as Christianity and Judaism held the same stance.
Asked if he believed homosexuality was harmful to society, he said: "Certainly it is a practice that in terms of health, in terms of the moral issues that comes along in a society - it is. It is not acceptable."
"Each of our faiths tells us that it is harmful and I think, if you look into the scientific evidence that has been available in terms of the forms of various other illnesses and diseases that are there, surely it points out that where homosexuality is practised there is a greater concern in that area."
At the time, Peter Tatchell, of gay rights group OutRage!, said: "It is tragic for one minority to attack another minority."