Nilesh Rane, son of Maharashtra Revenue Minister Narayan Rane, was on Sunday night booked for negligent driving.
His car hit and injured a policeman at Carter Road in suburban Khar, a senior police official said.
Mumbai Police Commissioner A N Roy said a case has been registered against Nilesh and added that the constable who was injured sustained minor injuries.
Police sources identified the injured constable as Bhagwan Jadhav and said that he was returning from duty when the accident took place last night.
