The Police Federation magazine cartoon shows officers taking their shoes off outside a mosque, as a bearded man escapes clutching bags of explosives.
Bedfordshire's chief constable Gillian Parker has written to complain.
The magazine's editor has apologised and said there was no intention to cause offence.
The cartoon was seen by Bedfordshire Police as an attempt to mock the force's advice to officers to remove their shoes before entering Muslim properties.
Ms Parker wrote: "The stereotypical portrayal of religious communities and the use of places of worship in a sacrilegious manner are bound to offend.
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She said: "We have worked hard over an extended period of time to achieve relationships and I feel that the stereotypical portrayal of Muslims as terrorists has unnecessarily jeopardised this.
"Where it is feasible to do so we continue to consider the individual customs of all communities when we enter their homes and places of worship; I make no apology for this."
Metin Enver, editor of the magazine, told the BBC: "Much of the material we publish comes from independent parties and is not necessarily the view of the Police Federation.
"However, we do apologise sincerely if the cartoon featured caused any offence to anyone.
"The idea behind it featured five different scenarios.
"It was supposed to depict how policing has changed over the years and how the police service takes account of different cultures.
"We did not intend to offend any of those groups highlighted in the cartoon."
The cartoon was published in the September edition of the magazine.
When this fad ends there's going to be a backlash. It won't be funny to others though there might be some around these parts who laugh. Come on, who's stupid enough to pander forever to murderers? Not even the English will put up with this crap forever. If we don't hammer the Muslims soon the hammer will come down sooner or later anyway, and then it's going to be terrible. Wake up. This fad is beyond stupid.