The Jets say they are aware of the arrest and are gathering information.
State police say Goodson was a passenger in a vehicle driven by 31-year-old Garant Evans of Roselle. Police found them stopped on Interstate 80 in Denville at about 3:15 a.m. Friday.
Sgt. Adam Grossman says both men were charged with marijuana possession, drug paraphernalia possession and weapons offenses stemming from a handgun found in the vehicle.
Evans is charged with DWI and another weapons offense.
Both men are held pending transfer to the Morris County jail.
Goodson played three seasons for Carolina and one for Oakland before the Jets signed him to a three-year deal this offseason.