Brown was carted off in the third quarter after catching an 18-yard touchdown strike from backup quarterback Charlie Whitehurst, cutting the Cowboys' lead to 10-7. Brown left the game with two catches for 31 yards.
Brown is viewed in San Diego as an heir apparent to Vincent Jackson. The 2011 third-round draft pick finished last season with 19 catches for 329 yards and two scores, and he's expected to play a larger role this season.
Brown generated significant buzz during training camp amid whispers that he was outplaying starter Robert Meachem.
"He's had a great offseason, he's in the middle of having an outstanding training camp, and he obviously is a playmaker," Chargers coach Norv Turner told the team's official website earlier in the week.
UPDATE: Kevin Acee of U-T San Diego reported Brown suffered a broken ankle and will undergo surgery Sunday. He's expected to miss at least eight weeks, a significant blow to the offense. "He's our best receiver," one veteran told Acee.
Follow Marc Sessler on Twitter @MarcSesslerNFL.