Ofcom upheld two complaints from listeners about Leeds based Radio Asian Fever after presenter Rubina Nasir hit out at homosexuality and mixed faith marriages.
She said that homosexuals should be 'beaten up' and that a Muslim marrying a non-Mulslim was on 'the straight path to hellfire'.
The presenter, known as 'Sister Ruby', said: "What should be done if they do it? [practise homosexuality].
"If there are two such persons among you, that do this evil, the shameful act, what do you have to do? Torture them; punish them; beat them and give them mental torture."
"Allah states, 'If they do such a deed [i.e. homosexuality], punish them, both physically and mentally.
"Mental punishment means rebuke them, beat them, humiliate them, admonish and curse them, and beat them up. This command was sent in the beginning because capital punishment had not yet been sent down."
She was while giving her interpretation of a Qur'anic verse and Ofcom got an independent translation from the original Urdu into English.
In a broadcast the following day she focused her attention on another Qur'anic verse and said it was critical of mixed-faith marriages.
She said: "What happens when a Muslim man or woman get married to a Mushrak [a follower of another religion).
"Listeners! Marriage of a Muslim man or woman with a Mushrak is the straight path to hellfire.
"Have my sisters and brothers, who live with people of bad religions or alien religions, ever thought about what would become of the children they have had with them - and the coming generation?
"Where the filth of shirk (the sin of following another religion) is present, where the dirt of shirk is present, where the heart is impure, how can you remove apparent filth. How many arrangements will you make to remove the apparent filth?
"We are saying that Mushraks have no concept of cleanliness and uncleanliness."
The broadcast was aired last but Ofcom announced its sanction after an investigation.
Ofcom said it regarded the comments as serious breaches of the broadcasting code and therefore a financial penalty should be imposed.
It added: "The content of the programme broadcast on 17 August 2011 included two statements which Ofcom considered were likely to encourage or to incite the commission of crime against homosexuals and were likely to encourage others to copy unacceptable behaviour towards homosexuals."
The radio station is also required to broadcast a statement of Ofcom's findings, on a date and in a form to be determined by Ofcom.
The financial penalty is payable to HM Paymaster General.