The rapist is believed to have committed five assaults since October, the local.fr reported.
Authorities said rumors circulating through social media of a serial rapist prompted them to go public.
The heads of local universities have told students not to go out at night by themselves.
The attacks have occurred about midnight in Lyon's Eighth Arrondissement. In each instance, victims have been threatened with a knife by an attacker wearing a hood, police said. Some of the victims have been cut.
The last reported attack occurred in late January.
Notable deaths of 2014 [PHOTOS]