Sir Iqbal Sacranie, head of the Muslim Council of Britain, will not be charged over allegedly homophobic remarks made in a BBC radio interview, police say.
Sir Iqbal Sacranie made the comments in a 3 January broadcast
Police investigated comments made on Radio 4's PM programme after a complaint from a member of the public.
Earlier this month, he told the programme he believed homosexuality was "not acceptable".
A Met Police spokesman said there would be no further action "on the advice of the Crown Prosecution Service".
Following the programme, in which Sir Iqbal also denounced same-sex civil partnerships as "harmful", officers said they would examine the remarks to see if an offence had been committed.
Speaking about civil partnerships, Sir Iqbal told the 3 January programme: "It does not augur well in building the very foundations of society - stability, family relationships. And it is something we would certainly not, in any form, encourage the community to be involved in."
He 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."
He said everyone in society should be tolerant, and if they are not happy then engage in the democratic processes to give their views.
"We may not be happy with the views being expressed by others. But the difficulty comes in that at the end of the day we are human beings."
He said both the opponents and supporters of civil partnerships had the right to speak out.
The Muslim Council of Britain said it was "naturally very pleased" by the police decision.
"To be honest, we thought it somewhat surprised when we heard that Sir Iqbal was being investigated by the police for merely articulating the mainstream Islamic viewpoint about homosexuality.
"We believe it is very important for faith leaders like Sir Iqbal to uphold the integrity of the family unit and underline its role in strengthening society."
After the interview was broadcast, Peter Tatchell, of gay rights group OutRage!, said it was "tragic for one minority to attack another minority".
"Both the Muslim and gay communities suffer prejudice and discrimination," he added.
"We should stand together to fight Islamophobia and homophobia."