Interior Minister Gerald Darmanin said the policeman was wearing a bulletproof vest and was not injured.
The attacker was "neutralised", he said, but added nothing more about the assailant or a possible motive.
BFM TV, citing a police source, said the attacker opened the door of a police car stationed in front of the police station and stabbed the policeman at the wheel with a knife.
He then tried to attack a second policeman in the car but a third policeman in the vehicle opened fire, seriously injuring the attacker, it said.
The suspect had Algerian nationality and was born in 1984, reported BFM TV and Le Figaro.
BFM TV added he was unknown to French authorities, while Le Figaro said he had an Italian residency permit.
Darmanin said he would travel to the scene of the attack in the Mediterranean resort city later on Monday morning.
Concerns about violent crime and terror attacks are among voters' main concerns in the run-up to a presidential election next year.
The attack coincides with the trial of Salah Abdeslam, the only surviving member of the Islamic State cell that carried out the gun-and-bomb attacks on bars, restaurants, the Bataclan concert hall and the Stade de France stadium on Nov. 13, 2015 that killed 130 people.
"I am going to the scene immediately this morning and I offer my support to the national police and to the city of Cannes," Darmanin said on his Twitter account.
BFM TV and Nice Matin newspaper cited a police source as saying the suspect said he had carried out the attack "in the name of the Prophet" Mohammad, hinting at possible Islamist extremist links.Â
