Four others were also arrested for mugging.
Detective Branch spokesman Monirul Islam said on Friday they were arrested in drives on Dhaka University campus and Shahbagh on Thursday night.
He said replicas of pistols, handcuffs, walky-talkies, and a bomb were seized from the fake detectives.
They were identified as Shahidul Islam Gazi, his brother Monir Gazi, Abul Kalam and Tara Mia.
DB’s Islam said they had searched people and taken away money and valuables by issuing threats.
The Gazi brothers had been arrested on the same charges and were out to commit the same crime when freed on bail, the DB official said.
He also said the suspected muggers held from Shahbagh were identified as Oli Ullah, Mohidul Islam, Habibur Rahman and Nayeb Ali.
The car they were riding was also seized, he added.