Coach Mark Richt said Sunday that Wood, a sophomore who has played in every game as a backup, will miss Saturday's game at No. 11 LSU.
Another Georgia player, injured offensive lineman Vince Vance, was arrested for driving with an expired license on Saturday night.
Wood, 21, told Richt he was parked while waiting to pick up his girlfriend and her friend on Saturday night and then drove away with just his parking lights on, according to Richt. Wood was arrested by University of Georgia police and charged with driving without the required lights in addition to DUI.
Wood was booked into the Athens-Clarke County jail at 3:42 a.m. and released at 9:16 a.m., according to the jail's booking report.
"Brandon certainly made a bad error in judgment to have alcohol in his system," Richt said.
"He made that mistake. He'll pay the price. He certainly won't be playing in this ballgame coming up here."
Wood has 10 tackles and seven quarterback hurries.
Richt said he hopes to have another defensive tackle, Kade Weston, back after Weston missed Saturday's 24-14 win over Vanderbilt with an injury.
Richt said he would not comment on Wood's status for the Nov. 1 game against Florida in Jacksonville.
Vance is out for the rest of the season with a knee injury.
Richt said Vance said he didn't realize his license expired on Oct. 11, his 21st birthday.
Richt said he was told Vance was pulled over because "he did not stop very well at a stop sign." He was then arrested for the expired license.
"I said 'Is there an outstanding ticket or anything like that you know of?' He said no. I'm just going by what he said to me."