Authorities say the accident, which they described as a fender-bender, occurred around 8:30 p.m. on Route 4 in Teaneck. The cause of the crash remained under investigation Saturday.
The other motorist, driving a Nissan Maxima, also wasn't injured.
NFL Network insider Albert Breer also exchanged text messages with the player's agent, Doug Hendrickson, who wrote: "Tuck's fine. Minor accident, that's it. He is playin."
Tuck was listed as probable for the game with a chest injury unrelated to the accident.
The Associated Press contributed to this report.