Ofcom ruled that Noor TV, which broadcasts on Sky, had breached broadcasting codes by inciting violence during a programme aired on May 3 last year.
The watchdog said the size of the fine reflected the seriousness of the channel's transgression, but stopped short of revoking its licence.
Presenter Allama Muhammad Farooq Nizami was hosting a phone-in when he was asked what the punishment was for anyone showing disrespect for Prophet Mohammed.
"There is no disagreement about this," he replied. "There is absolutely no doubt about it that the punishment for the person who shows disrespect for the Prophet is death."