Mason was arrested on suspicion of misdemeanor reckless driving, possession of marijuana, resisting an officer and failure to register a motor vehicle, according to a report filed by the Broward County Clerk of Courts.
"We are very disappointed to learn of an incident involving Tre Mason in the Miami, Fla., area Saturday afternoon," the Rams said Sunday in a statement. "We are in the process of obtaining more information about the facts surrounding this incident and will have no further comment at this time."
The Rams on Friday held their first team meeting in Southern California since their move from St. Louis was approved in January. About 80% of the roster attended the voluntary meeting at a Manhattan Beach hotel, Coach Jeff Fisher said afterward. Some players said they planned to investigate housing options this weekend.
The Rams on Sunday declined to confirm whether Mason attended the meeting.
Mason is preparing for his third season with the Rams. The former Auburn star was selected in the third round of the 2014 NFL draft.
On Sunday, police in Hollywood, Fla., told the Associated Press that an officer started following Mason on Saturday afternoon after seeing him drive a Porsche at more than twice the speed limit in a 35-mph zone. The officer said Mason drove away from him and stopped only when his car was blocked by another vehicle.
Officers said they used a stun gun twice during Mason's arrest after he refused to cooperate. Mason refused to give his name or provide his driver's license, an officer said. The officer also said he smelled marijuana in Mason's car.
Mason rushed for 207 yards and a touchdown in 75 carries last season. He also caught 18 passes for 88 yards.
Mason played behind Todd Gurley, the NFL's offensive rookie of year who rushed for 1,106 yards and 10 touchdowns. Receiver Tavon Austin rushed for 434 yards and four touchdowns. Running back Benny Cunningham rushed for 140 yards.
At last month's NFL scouting combine, Fisher was asked how important the next few months were for Mason, who as a rookie in 2014 led the team with 765 yards rushing, averaging 4.3 yards per carry.
"Tre's going to have, got to have, a great off-season program," Fisher said, adding, "We drafted Tre for a reason and I think when you look at our running back position, when you talk about Todd and then Tre and then Benny, I mean I think that's as good a group as you'll find in the league from a depth standpoint and the difference in their abilities and what they do.
"I think Tre realizes it. He's got to put the commitment in wherever he is and get ready for camp and have a great preseason."
Staff writer Matt Wilhalme contributed to this report.
Follow Gary Klein on Twitter @LATimesKlein