Goodson, 26, and Garant Evans, 31, were arrested in May after New Jersey state police found them intoxicated in a sport utility vehicle stopped in the center lane of Interstate 80, the Newark (N.J.) Star-Ledger reported.
A small amount of marijuana was found in Goodson's possession.
A loaded .45-caliber handgun loaded with a hollow point bullet was found in the vehicle's glove box, the Morris County Prosecutor's Office said. Neither man claimed ownership of the gun.
Both men had been indicted on charges of second-degree unlawful possession of a weapon and fourth-degree unlawful possession of a prohibited weapon, the bullet.
Evans pleaded not guilty during the same court appearance.
The NFL had suspended Goodson for the first four games of the 2013 season for violation of the league's substance abuse policy.
After returning from suspension, Goodson played in just two games before tearing ligaments in his left knee and requiring surgery. He was out the rest of the season, having made seven carries for 61 yards and two catches for 19 yards.