State police said a tow truck operator driving on Route 80 in Denville called 911 after seeing the SUV, where Goodson was a passenger, stopped in the left lane on the highway shortly after 3 a.m. Troopers responded and arrested the driver, who has a prior felony conviction, on a DWI charge.
Authorities found the gun and drugs in the car while they were evaluating Goodson, state police said.
Goodson and the driver were both charged with possession of a handgun, hollow point bullets, marijuana and drug paraphernalia. Information on attorneys wasn't immediately available.
A team spokesperson told NBC 4 New York the Jets "are aware of the report and are gathering information."
The Jets, looking to upgrade their running game, signed the versatile Goodson and traded for hard-running Chris Ivory, formerly of the Saints, this offseason to complement third-year man Bilal Powell and Joe McKnight, who is in his fourth year.
Goodson, who will turn 26 next week, had been expected to serve as the second RB on the depth chart behind Ivory going into training game, and was widely viewed as a boon for the passing game.
The Jets signed him to a three-year $6.9 million deal in March to help replace Shonn Greene, who was signed by the Tennessee Titans in free agency, in the backfield.
Goodson was drafted by the Carolina Panthers in the fourth round of the 2009 draft and most recently played for the Oakland Raiders. He missed most of last season due to an ankle injury, but compiled 221 rushing yards on 35 carries and caught the ball 16 times for 195 yards in a touchdown in 12 games, mostly as Darren McFadden's backup.