The 29-year-old French man was arrested at the scene of the attack, which occurred in the suburb of Colombes, northwest of Paris, and was in custody, the prosecutor said. The two police officers were injured and taken to hospital.
A letter containing a pledge of loyalty to Islamic State was found in the suspect's car, as well as a knife, the department said. It did not say if he had been formally charged.
The man, who has not been named, was not previously known to intelligence services as a radicalization risk, according to the department's statement.
The officers had been stationary and conducting routine checks when they were hit by a black BMW.
Footage of the scene of the attack on the website of daily newspaper Le Parisien showed one police motorbike sandwiched between the crumpled bonnets of a police car and the BMW. Debris from a second bike lay strewn on the road.
France has experienced a wave of attacks by Islamist militants in recent years.Bombings and shootings on November 13, 2015 at the Bataclan theatre and other sites around Paris killed 130 people, and in July 2016 an Islamist militant drove a truck through a crowd celebrating Bastille Day in Nice, killing 86.