The man, only identified as Theo, told BBC he was leaving his house in the suburb of Aulnay-sous-Bois when he was stopped by police doing identity checks that are believed to target drug dealers.
The detentions took place across the Seine-Saint-Denis department, the administrative center of which is Bobigny, the French Europe 1 broadcaster reported citing a police source on Sunday.
However, an investigating magistrate has charged one of the police officers with rape and is still examining the case.
The young man - who is still hospitalized - says he was sodomized with a police baton.
An image grab taken from an AFP video shows a van of French radio station RTL burning during clashes on the edge of a rally to denounce police brutality in Bobigny, outside the French capital, Paris, February 11, 2017.
The case has revived past controversies over the relationship between police and immigrant communities in rundown suburbs. Around 10,000 cars were burned and 6,000 people were arrested.
Police officials have insisted the incident was a weird accident, according to AFP, saying officers were "applying a truncheon blow horizontally across the buttocks" and "there are insufficient elements to show that this was a rape".
President Francois Hollande has visited Theo in hospital and Prime Minister Bernard Cazenueve said Wednesday the government expressed its "solidarity" with the alleged victim.
She added: "It's just simply abnormal and so I think these clashes are nothing compared to what people should do".
As well as damaging cars, protesters also destroyed store fronts and produce. "Everything, my whole investment is gone". Four police officers have been suspended pending an inquiry.