Brown was injured during Saturday night's 28-20 preseason victory against the Dallas Cowboys when his foot appeared to get caught under a tackler after his 18-yard touchdown catch in the third quarter.
Brown was carted off the field.
In addition, starting running back Ryan Mathews broke his collarbone on his first carry of the preseason Aug. 9, and is questionable for Week 1.
"I think we're equipped to handle whatever comes our way and we'll have guys step up and fill his shoes," Chargers coach Norv Turner said Saturday.
Brown had 19 receptions for 329 yards and two TDs in 14 games as a rookie last season for the Chargers.
Information from The Associated Press was used in this report.