In a widely circulated video on social media, the officer can be seen taking the images down from a wall outside a construction site in Crumpsall, north Manchester, an area with a large Jewish population.
The video was posted to social media by North West Friends of Israel on X, formerly known as Twitter, on Monday.
In a statement on Tuesday, GMP confirmed the actions went against guidance issued to the police, and that an investigation was underway.
Assistant Chief Constable Wasim Chaudhry, of GMP, said: “We share concerns raised regarding the removal of posters in the north Manchester area and can confirm that an investigation is under way.
“The action taken last night, in response to complaints, is contrary to guidance that the force had already issued to staff in relation to flyposting.
“We will continue to work with local authorities and the community to ensure posters can be displayed. We regret any offence caused.”
A large number of posters of people kidnapped from Israel by the terror group Hamas have gone on display since violence erupted in the Middle East earlier this month.
— Adam Ma’anit (@adammaanit) October 30, 2023
On Monday, the Metropolitan Police also faced a backlash online after its officers were seen removing kidnap poster in Edgeware, London.
In a statement, the Met said the force recognised people wanted an explanation.
It said locals believed the posters were put on specific shop shutters in retaliation for comments about the Israel-Hamas conflict made on social media by a person associated with the business.
Residents told police they were concerned it would escalate an already tense situation.
The Met said: “Officers went to the shop and, acting in good faith, they removed the posters in an effort to prevent any such escalation.
There's a photo/video being shared online of officers removing posters of those kidnapped in Israel from the shutters of a shop in Edgware.
We totally understand the concerns raised, but we believe the officers were acting in good faith here.
We've set out what we know below:
— Metropolitan Police (@metpoliceuk) October 31, 2023
“The removal of these posters elsewhere in London has caused anger and upset in recent weeks.
“We know a photo of our officers doing the same will cause further concern, particularly for anyone not aware of the full facts reported to us at the time.
“We have no wish to limit the rights of anyone to protest or to raise awareness of the plight of those kidnapped and the terrible impact on their families.
“But we do have a responsibility to take reasonable steps to stop issues escalating and to avoid any further increase in community tension.
“On this occasion, that is what officers were trying to do.”