Goodson didn't participate in practice -- he didn't even watch, according to a league source -- but he met with team officials.
Technically, OTA practices are voluntary, so Goodson couldn't be held out as a punitive measure. One source described it as a mutual decision, with the understanding that football shouldn't be his primary focus right now.
Goodson's future with the team appears uncertain. Owner Woody Johnson, speaking to reporters at the NFL meetings in Boston, said the team still is investigating the matter.
"We're at a point of investigating the facts," Johnson said to reporters, according to USA Today Sports. "[General manager] John Idzik met with him this morning, he'll meet with the coaches today. We'll try to get the story on what the facts are and go from there."
Johnson quoted the famous "Superman" slogan, saying the Jets have a "strong credo."
"We're trying to win games and do the right thing. Truth, justice and the American way. We live by it, we really do," he told reporters.
Goodson was arrested at 3 a.m. Friday during a traffic stop on Route 80 in New Jersey. He was the passenger in a car that was stopped in the left-center lane. Goodson was charged with unlawful possession of a handgun, possession of a loaded handgun, possession of hollow-point ammunition, possession of marijuana and drug paraphernalia.
Both Goodson and the driver, Garant Evans, 31, of Roselle, N.J., were intoxicated, according to police. Goodson required medical attention at a local hospital.
After more than 12 hours in jail, Goodson was released on $50,000 bail.
The New Jersey State Police hasn't determined who owns the gun, according to a police spokesman who said that investigation is ongoing.
Goodson is scheduled for a pre-indictment conference on June 12, according to the Morris County Superior Court. That falls on the second day of the Jets' three-day, mandatory minicamp. Goodson still hasn't retained an attorney, according to court records.
If Goodson pleads guilty or is convicted of unlawful possession of a handgun, he will be subject to the Graves Act, a New Jersey law that carries a minimum mandatory sentence of three years. There is a chance the charges could be amended.
New Jersey also has some of the strictest sentencing requirements in the nation for possession of hollow point bullets. If convicted of the charge, Goodson could face a five-year mandatory minimum sentence according to Jenny Carroll, an associate professor of law at Seton Hall Law School, where she teaches criminal law. The gun charge could be dropped for either Goodson or Evans if the police determine who it belonged to, but Carroll said both occupants of a vehicle can still be found guilty of charges relating to one gun or hollow point bullets under a clause called constructive possession.
Goodson, whom the Jets signed to a three-year, $6.9 million contract in March, also could face harsh penalties from the NFL. The league is reviewing the matter, a spokesman said.
The NFL mandates that each team has a preseason meeting with players where team officials and law enforcement go over local gun laws. The NFL discourages all players from owning guns but stipulates that all players who do choose gun ownership must have them legally registered.
The Jets had not yet held their annual meeting at the time of Goodson's arrest, according to a source. The Jets declined to confirm.
Goodson would have been through the session, however, with his previous teams, the Carolina Panthers and Oakland Raiders. The NFL's program has been in place since the 1990s, which was before Giants wide receiver Plaxico Burress was imprisoned stemming from a night when he accidentally shot himself in the leg in New York City. Goodson, who is from Texas, might not have been aware of just how stringent local laws are around the Jets' facility.
Goodson's contract included a $1 million signing bonus. A source said Goodson has yet to receive the full amount, per the payment schedule in the contract, but he has received at least $500,000. If the Jets decide to cut him immediately, before the matter is adjudicated, it will be difficult to recover the bonus money.
A Jets spokesman said last week the team wouldn't comment "until the legal process has run its course."
The Jets signed Goodson, 25, who played last season with the Raiders, with the idea that he'd team with Chris Ivory to form a one-two punch in the backfield.
ESPNNewYork.com's Jane McManus contributed to this report.