The running back, who is facing serious legal issues, was placed on the reserve-did not report list as the players arrived for training camp at SUNY Cortland on Thursday.
NFL.com's Ian Rapoport reported that Goodson's absence is unrelated to his recent arrest, that he is addressing a few "personal matters" and the team is being supportive.
Goodson, signed as a free agent in the offseason, was arrested on drug and weapons possession charges in May along with a friend in New Jersey. The case was sent to a grand jury last month. It was not immediately certain if Goodson's absence was related to his legal situation.
Coach Rex Ryan said in a statement after media availability Thursday that the team knew Goodson wasn't going to report to camp on time and "we understand why he's not here." The team provided no further details.
Goodson's agent did not immediately respond to an email sent by The Associated Press seeking comment.
Goodson, who played last season with Oakland, was arrested with Garant Evans after they were found in a car stopped on Interstate 80 in New Jersey. The men were charged with marijuana possession, possession of drug paraphernalia and weapons offenses. Police said they found a .45-caliber semi-automatic handgun and a hollow-point bullet in the vehicle.
The 25-year-old Goodson has pleaded not guilty and took part in some preseason practices with the Jets, who signed him to a three-year, $6.9 million deal.
The Associated Press contributed to this report.