The cause of the injury has not been confirmed but eyewitness claim he picked up a tear gas grenade that exploded in his hand.
Police say he is being treated in hospital, euronews reported.
Clashes erupted on the Champs-Elysees between protesters and law enforcement with the latter reportedly using batons and pepper spray.
The protests - which were originally against the rise in diesel costs - have turned into a general discontent against French President Emmanuel Macron and high living costs.
Various events were also planned in other cities, including Montpellier, Lille, Nantes, Rennes, Brest, Caen and Lorient.
