Brown, 28, was arrested at 4:29 a.m. Saturday, Marietta Police Officer Jennifer Murphy said. Marietta is located about 15 miles northwest of Atlanta.
Brown has an initial court appearance scheduled for May 13. Murphy said Tuesday that the date is tentative and Brown might not have to appear in person.
Brown's mother, Joyce Brown, told The Associated Press in a telephone interview Monday that her son was visiting his hometown of Cartersville for her and her husband's 32nd anniversary. She said he had eaten dinner with relatives and then went to a club. She didn't know the name of the club, but the night wasn't part of the anniversary celebration.
She said her son was pulled over for failing to use a turn signal, but she believes he was targeted because he was driving a high-priced car and is black.
Brown's mother said she believes both police and the media unfairly single out football players.
"Just because of who they are, they shouldn't be pinpointed," Brown said. "They're still people, too."
Murphy wouldn't provide details of the arrest, and the AP has filed an open-records request for the information. Officials at the Smyrna City Jail say Brown posted $1,110 bond and was released hours after his arrest. Cartersville is located about 20 miles from Marietta.
Brown's agent, Todd France, didn't immediately return phone and e-mail messages seeking comment. A team spokesman had no comment on the arrest. Brown's mother said her son had an attorney, but she wouldn't give a name.
Dolphins owner Stephen Ross, who is attending the NFL Annual Meeting in Orlando, Fla., said the organization is unhappy about the recent spate of arrests of its players. Cornerback Will Allen was charged with driving under the influence in Miami Beach, and defensive tackle Tony McDaniel was accused of domestic violence at his home in Davie, both last month.
"It certainly doesn't make us happy, and it is a concern," Ross said without specifically talking about Brown. "I think the coaches and (Dolphins football czar) Bill Parcells are disappointed and concerned, and they are addressing it."
Brown's 2009 season ended early with an injury to his right foot. He was the Dolphins' leading rusher at the time and was the key player in their Wildcat formation before being placed on injured reserve Nov. 18.
Brown had 648 yards on 147 carries and eight touchdowns last season before he was injured. He has 4,081 rushing yards and 31 touchdowns in his five-year NFL career.
Copyright 2010 by The Associated Press