The police are deciding whether to investigate whether a joke broadcast on last week's Have I Got News For You was homophobic.
However, the BBC said the gag was designed to show up the persecution of homosexuals in Iran.
One viewer complained following the comment, which came amid a discussion over a failed Iranian bid to create to the world's biggest ostrich sandwich.
Host Alexander Armstrong said: ‘On the plus side they do still hold the record for hanging homosexuals.
And guest Skinner joked that homosexuals are often ‘ostracised;.
A spokeswoman for the Metropolitan Police confirmed: ‘A member of the public has made a complaint regarding comments made in the programme. The complaint is currently being reviewed.’
But the BBC said: ‘The presenter never intended for this comment to be homophobic - quite the opposite.
‘Viewers are more than familiar with HIGNFY use of satire - in this instance aimed at the Iranian regime and not the Iranian gay community.’
According to PinkNews.co.uk, the complaint was lodged by viewer Lionel Wright from London, who sad he was ‘sickened’ by the BBC.
He said: "I'm a middle-aged gay man… I'm surprised and sickened that the BBC - funded by a licence fee to which millions of lesbian, gay, bisexual and transgender people contribute - should broadcast reactionary, hate-filled remarks which celebrate the slaughter of human beings on the basis of their sexuality.
‘The episode leaves the viewer wondering: if the BBC condones the broadcast of statements like this, will it also disseminate “jokes” by racist comedians which applaud the lynching of African Americans in the Southern states of the USA?’
Buy gay rights activist Peter Tatchell tod the website: ‘I interpreted it as an anti-Iran joke, exposing and mocking Iran's murderous homophobic regime. It was parody and satire, I think, not an endorsement of executions.’
Human rights activists estimate that as many as 4,000 people, some of them children, have been executed in Iran for being gay.
The offending comment comes 8mins, 45 seconds into this clip: