The Glasgow Warriors front-rower has been forced to go under the knife to resolve the problem and is now set for a lengthy spell on the sidelines.
Brown is unlikely to feature in Scotland's autumn internationals in November, with head coach Gregor Townsend's side set to face Samoa, Australia and New Zealand.
Edinburgh star Ross Ford, who featured in Scotland's summer tour of Singapore, Australia and Fiji, is likely to continue in the number two jersey for the November Tests.
Meanwhile, the rest of the Scotland stars have returned to training with the other members of the Glasgow squad.
British & Irish Lions winger Tommy Seymour has been given more time off due to his efforts in New Zealand and is set for a return to the Warriors set-up next month.