The backbencher, who represents Bradford West following his by-election victory in March, has tabled a parliamentary motion at Westminster outlining his concerns, saying the officer from the Met Police's SO15 unit entered his home "without his knowledge or consent" and slept there.
The Respect MP says an individual working in his office acted as the officer's agent and that the policeman "operated under an alias" against him on Facebook and elsewhere "all the while concealing that he was a senior serving police officer at Scotland Yard".
Mr Galloway is calling on Home Secretary Theresa May to make a Commons statement on the matter.
On his website, the former Glasgow Kelvin MP claims he has evidence that the officer has been "feeding disinformation aimed at damaging me to a national newspaper and to others, aided by a member of staff in Bradford". Mr Galloway said he had also written to Bernard Hogan-Howe, Met Commissioner.
Mr Galloway said: "It could not look worse than that a person, whose job is essentially to police Britain's Muslim community, could have been coming and going, sleeping in my house when I was away, when I am the MP for tens of thousands of Muslims and heavily involved in issues that vitally affect the Muslim community."
Scotland Yard said it had received a complaint from a member of the public: "A voluntary referral is being made to the Independent Police Complains Commission. The officer has been placed on restricted duties pending the outcome of the investigation."