Vick reluctantly surrendered a water bottle that smelled like marijuana and contained a substance in a hidden compartment to security at Miami International Airport.
He was not arrested and was allowed to board a flight that landed in Atlanta before noon Wednesday.
Miami police said Thursday it could be weeks before a decision is made on whether to file charges against the three-time Pro Bowler, who this season became the first quarterback in NFL history to rush for 1,000 yards.
Under Florida law, possession of less than 20 grams of marijuana is a misdemeanor punishable by up to a year in prison and a $1,000 fine. First offenders rarely do any jail time.
"We'll do an analysis and see what it is. There's no sense of urgency to it," Detective Alvaro Zabaleta said Thursday.
The NFL's substance abuse policy states any team can decide that a player's "behavior, including but not limited to an arrest," can warrant a physical exam from its appointed medical director. NFL spokesman Greg Aiello said no decision had been made in Vick's case.
"We have a process that provides guidelines for every situation," Aiello said. "Our doctors conduct a lengthy evaluation, if necessary, and then decide if enrollment in a treatment program is necessary."
Vick did not return a phone call Thursday. The Falcons said they would have no further comment until they discussed the matter with Vick, who finds himself mired in another embarrassing situation.
Last April, Vick settled a lawsuit filed by a woman who claimed the player knowingly gave her herpes.
In November, Vick made an obscene gesture toward Atlanta fans who heckled the team as it came off the field after a 31-13 loss to New Orleans. Vick apologized profusely, paid a $10,000 team fine and donated another $10,000 to charity.
The bottle was found to have a compartment that contained "a small amount of dark particulate and a pungent aroma closely associated with marijuana," a Miami police report said. The compartment was hidden by the bottle's label so that it appeared to be a full bottle of water when held upright, police said.
Associated Press writer Curt Anderson in Miami contributed to this report.