Bennett, 25, was arrested on suspicion of public intoxication and taken to the city detention center, Dallas police said.
Police said that shortly after 6 a.m., officers responded to reports of a man banging on doors. The location given by police was a community of town homes near downtown Dallas.
Last week, Bennett told reporters that he would be training for his pro career in Fort Worth, which is about 30 miles west of Dallas.
It was unclear whether he had been released from the detention center. An attempt to reach someone at the detention center was unsuccessful.
Earlier this month, Bennett threw two touchdown passes and ran for two scores in the first half as No. 1 Georgia demolished No. 3 TCU 65-7 to win the College Football Playoff national championship.
Bennett walked on at Georgia nearly six years ago at the beginning of its growth into college football’s most dominant program.
The University of Georgia athletic department did not immediately respond to a request for comment.