One scene that particularly provoked anger was where a heavily-made up girl rushed to put on a hijab and pretended to be reading the Koran when her father entered.
The six-part series follows the fortunes of a Muslim community leader and aired for the first time on BBC1 on Monday. It has been created by British Muslim Adil Ray, who also plays the lead role of Mr Khan, reported Daily Mail.
The comedy mocks Mr Khan's self-importance, including his delusions about his position in the community and about his standing in the business world.
One viewer wrote on BBC's messageboard: "This is terrible stereotyping, ignorant and just dreadful."
Another said, "HIGHLY disappointed especially when her father walks in and she dis-respectfully opens the Koran!!"
But there were others who defended the show. One said, "People are reading too much in to Citizen Khan, especially the hijab thing, it happens!"
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Critics have complained that it repeats many stereotypes about British Muslims, with the first episode all about the troubled wedding plans of one of Mr Khan's daughters, Shazia.
A BBC spokesman said, "Citizen Khan has made a very positive start, launching successfully with 3.6million viewers and a 21.5 per cent share in a late-night slot.
"New comedy always provokes differing reactions from the audience. The characters are comic creations and not meant to be representative of the community as a whole."