The incident happened Saturday evening around 9 p.m. in Beverly Hills, according to the Beverly Hills Police Department.
It's unclear what prompted Edelman to jump onto the car but he did cause "damage," police added.
Police arrested him for misdemeanor vandalism, reports say.
Edelman was released on a citation and is scheduled to appear in court on April 13.
The Patriots wide receiver was last year's Superbowl MVP.
On Instagram, Celtic's star Paul Pierce posted this photo of him and Edelman the same evening.