In one case, reported by German broadcaster NDR, a shackled Moroccan man was allegedly forced to eat rotten pork off the floor at a police station.
Earlier, a policeman allegedly bragged on the WhatsApp messaging service that he had made an Afghan man choke until he "squealed like a pig".
The reports have shocked officials.
A police officer's home and workplace have been searched and investigators found a photo on his mobile phone showing a man being held down in a painful stress position.
Witnesses are being questioned over the alleged abuses, according to NDR.
The head of human rights group Pro Asyl, Guenter Burkhardt, said the allegations indicated "an appalling level of racism and inhumanity".
In one WhatsApp message, quoted by NDR, the policeman wrote: "I knocked him away. An Afghan. With an immigration ban. Stuck my finger up his nose. And he choked. It was funny. And dragged him in shackles through the (police) station. It was so great. Squealed like a pig. It was a gift from Allah."
An unnamed police source was quoted as saying "there was often screaming from the holding cells, and when it got too piercing they didn't look into it - they just shut the door, to stop the sound getting out".
The German government official in charge of integration, Aydan Ozoguz, called the allegations "shocking".
She said that if a policeman had actually tortured migrants then the police must "make it absolutely clear that they do not tolerate such inhumane behaviour in their ranks".
Prosecutors in northern Germany are investigating alleged cases of police brutality towards migrants in the city of Hanover.