A driver has deliberately attacked a Paris policewoman outside the Presidential residence, the Elysee Palace, according to reports.

French media reported that four people abandoned the car after hitting the policewoman and two were arrested while a manhunt is being conducted for the other two passengers.

The officer was thrown onto the hood of the car and she obtained injuries to her wrist, knee and back.

"She [the injured policewoman] says that the driver looked at her in the eye and did not pull on the brakes, and that he voluntarily hit her. Three witnesses nearby say the same thing," eyewitness Stephanie Weber-Boyer told Europe 1.

"My colleague, who was a guard at the Elysee Palace, noticed a vehicle that was moving the wrong way. She approached. The vehicle hit her deliberately. My colleague fell on the hood of the car... and then fell to the ground," she added.

It remains unclear if the hit-and-run attack had any connection to last week's attacks on the offices of satirical magazine Charlie Hebdo.

French police officials could not be immediately reached for comment.