Foster was released Friday night on $2,500 bond.
A second-degree marijuana possession charge is considered a Class A misdemeanor in Alabama.
Tuscaloosa Police, in a news release Saturday, acknowledged officers encountered Foster and "found probable cause to arrest him." The release did not address whether he was pulled over, why police suspected he had marijuana or how much they say he had.
The 49ers released the following statement Friday night: "The San Francisco 49ers organization is aware of the matter involving Reuben Foster and we are currently gathering all relevant facts."
The arrest comes almost two weeks after Foster wrapped up a rookie season in which he finished second on the 49ers in tackles with 72 in 10 games.
Foster, who played college football at the University of Alabama, was the No. 31 overall pick in the 2017 NFL draft after the Niners traded into the end of the first round to get him. That came after Foster raised some red flags at the NFL scouting combine, in which he was sent home early after he got into an argument with a hospital worker and had a urine sample show up as diluted, which, according to the NFL's policy on substances of abuse, was treated as a positive test.
Because of the diluted sample, Foster entered the league in the substance abuse program.
After drafting Foster in April, 49ers general manager John Lynch said he "anticipated" people questioning Foster's off-field issues but felt good about making the pick anyway.
When Lynch was directly asked about the diluted sample, he made it clear he was not concerned.
"We spoke with Reuben about that and felt comfortable about that situation as well," Lynch said at the time.
The Associated Press contributed to this report.