Team spokesman Art Chase said in an email that the fifth-year senior was rushing the quarterback during Monday's scrimmage when he was hurt.
"When you have a great person, a great player and a guy that's a stalwart in the program that's had two knee surgeries, it's upsetting to say the least," coach David Cutcliffe said Monday in a statement. "Kelby is a very strong spiritual person too, so he'll be fine."
Brown entered his final season as the undisputed leader of a Duke defense that improved significantly last year during a surprise run to an Atlantic Coast Conference division championship. Brown was an all-ACC first-team pick and one of the league's top tacklers with 114 as Duke reached the ACC title game.
Brown suffered torn anterior cruciate and medial collateral ligaments in his right knee late in the 2010 season, then redshirted the 2012 season after tearing his right ACL again.
The Associated Press contributed to this report.