Brown sustained the injury in Sunday's 1-1 friendly draw against Rapid Vienna in Austria, with tests showing he had almost torn his hamstring clean off the bone.
The 29-year-old doesn't need surgery, but even so he will miss a minimum of eight weeks, ruling him out of this month's Champions League second-round qualifier with KR Reykjavik.
He will also sit out potential third-round and play-off ties should the Scottish champions progress that far.
Brown's injury is a major blow for Scotland boss Gordon Strachan as well.
The Scotland captain will definitely miss his country's opening Euro 2016 qualifier against World Cup finalists Germany on September 7 and faces a race to get fit for clashes with Georgia and Poland the month after.
Hoops manager Ronny Deila, quoted in several Scottish newspapers on Wednesday, said: "It's bad news for Scott
He will be out for two months, maybe three.
"The hamstring has been almost ripped off.
"He doesn't need an operation, which is a positive thing
But it is quite a big injury.
"It's hard for him and it's hard for us
But we can't do anything about it
We have to try to get him back on the pitch as quick as possible - but we have good midfielders who can step up."
Source : AFP
Source: AFP