Mounira Ben Ghazi, a senior supervisor at Mongi Slim hospital, named the dead man as Moez Dahmani, in comments made to Express-FM radio station.
Dahmani, who was born in 1986, died of gunshot wounds, Ben Ghazi said.
An interior ministry spokesman confirmed the death of a protester in comments broadcast on Hannibal TV but gave no further details.
Police and followers of the hardline Salafist movement Ansar al-Sharia clashed in Tunis and in the central city of Kairouan today after authorities banned the Islamists from holding their annual congrees.