Dozens of the flyers, which feature photographs of Shokat Lal, Fareed Hussain and Gulfraz Nawaz, were discovered pasted around Normanton yesterday morning.
The posters accused Pakistani community leader Mr Lal, Derby City Councillor Mr Hussain and former Jamia mosque secretary Mr Nawaz of a series of allegations.
Police are investigating whether a crime has been committed by whoever was behind the posters.
Mr Lal said he believed they had been put up by Muslim extremists.
He said: "I worry what it might inspire in people.
"We know Derby is a national hotspot for extremism. If we leave this unchallenged, the consequences could be quite severe.
"In Derby, there is a real undercurrent of radical views and it could lead to a fracturing of the society. They seem to want to isolate the Muslim community and undo the work we have done to unite people."
Mr Hussain, who represents Arboretum ward for the council, said it was not the first time the three had been targeted by extremists.
Mr Hussain said: "But it is the first time they have done it in this manner.
"We need to get people to understand just how extreme these people are – it is just because we have challenged some of their ideas."
Mr Lal added: "I think it is time we exposed this group of people who are more than prepared to benefit from the British way of life but only the bits that suit them."
Chris Williamson, MP for Derby North and Normanton representative for Derby City Council, said whoever put up the posters was "utterly reprehensible."
He said: "It is a pathetic attempt to undermine people of entirely good character.
"It is no small measure to say that these three men have helped to revive the economy of the area.
"They are extremely hard-working community leaders."
Sightings of the posters were reported to police at 9am yesterday and officers began combing the area, tearing down the flyers, with council staff hosing down the remnants afterwards.
Posters were put up on schools and mosques in Normanton and around nearby streets.
Superintendent Gary Parkin, of Derbyshire police, said the force was working closely with the three people featured on the posters.
He said: "We will be investigating if any offence has been committed and will be speaking to the three men to try and determine who is responsible."
Mr Hussain said that, previously, leaflets had been sent out to households in Derby speaking out against the work community leaders in Normanton had done.
Mr Nawaz said he had been shocked by the posters.
He said: "It is a very personal attack.
"If people have anything against us why don't they just talk to us?
"People are jealous. We are quite well known in the community and people don't seem to like us coming forward and taking an interest.
"I hope the police will do their utmost best to get these people."
