Labour's Rupa Huq criticised Citizen Khan's depiction of a "quite backward" family of Muslims.
The show was accused of stereotyping Muslims when it started in 2012 and its creator, Adil Ray, has told the Radio Times he had received death threats.
The BBC said the award-winning show had received much positive feedback.
But Ms Huq, MP for Ealing Central and Acton, whose sister Konnie is a former Blue Peter presenter, said: "I feel as if I didn't know what the year is ... you would think it's an everyday tale of a Birmingham family of Muslims but they're really quite backward.
"Again, the Islamophobic point [Labour MP Chuka Umunna] made, it's a beardy weirdy chap and they're not quite cutting off people's hands but I can imagine that being in a future episode."
Citizen Khan prompted complaints when it launched in 2012 and Mr Ray has previously said he had received abuse from people who believed it was making fun of Islam or stereotyping Muslims. [BBC] Read more
