Deputies found a bag of marijuana under the seat after stopping and searching the 2007 Dodge Charger that Smith, 22, was driving on U.S. Route 431, Henry County Sheriff William Maddox confirmed Monday.
"He was following too close and he had a tag light that was out," Maddox said. "The officer pulled him over and when he did, he smelled the odor of marijuana, so he searched the vehicle and found about a baseball-sized package of marijuana."
Smith and passenger Dazme Woods, 21, who also was arrested, were apparently headed for Florida for spring break. The two said late Sunday on Twitter that they were on their way to Panama City.
Smith was released on $2,000 bond at approximately 2:45 a.m. ET Monday. Woods was released on $3,000 bond. Woods' bond was higher because he was arrested last week for felony marijuana possession.
The Henry County Sherriff's office did not know whether Smith had an attorney.
Georgia coach Mark Richt said he spoke with Smith afterward, but added the conversation was brief due to a poor phone connection. Richt did not want to speculate on the details of the arrest or possible punishment until after learning more facts of the case.
"I don't know all the details yet, so I don't want to throw anybody completely under the bus yet, but I'm not thrilled that I'm having to deal with it," Richt said on the same day Georgia announced that he will receive a three-year contract extension.
Athletic director Greg McGarity said such an arrest typically carries a mandatory one-game suspension by the school, with Richt having the option to increase it to two games.
"In due time, we'll let you know what's going to happen with that," Richt said.
If Smith receives game punishment for the arrest, it will hit Georgia at a position where its depth is already thin.
Richt dismissed freshman defensive backs Nick Marshall and Chris Sanders last month for violating team rules. Senior Sanders Commings, who started all 14 games last season, is already suspended for the first two games for his role in a domestic dispute in downtown Athens in January.
Backup cornerback Jordan Love also transferred to Towson in the offseason.
Smith started seven games last season, making 24 tackles and two interceptions, and is expected to play a key role in the Bulldogs' secondary in the fall.
But if they are without seniors Smith and Commings early in the season, the Bulldogs will be left with sophomore Damian Swann, redshirt freshman Devin Bowman and Malcolm Mitchell, now a receiver, as the top choices at cornerback.
Georgia's coaches already hinted that Mitchell, who was second on the team with 665 receiving yards last season as a true freshman, would contribute on offense and defense in the fall.
Richt said Monday that Mitchell will now "work almost exclusively on defense" in spring practice, which starts next week.
"Malcolm's going to play a big role, I think, period, at corner, regardless of what happened with Branden," Richt said. "He's a very talented football player. We all know he's an outstanding receiver, but he's got some tremendous skills as a defensive back, as well."
David Ching covers Georgia athletics for DawgNation. Information from The Associated Press was used in this report.