As Celtic won their latest tour fixture, a 5-2 victory over Linzer ASK, reports from Austria suggested that Brown has been ruled out of action for up to three months.
That worst-case scenario would not only prevent him from taking any part in Champions League qualifying and the opening round of fixtures of the SPFL Premiership season, but would also threaten his involvement in Scotland's opening Euro 2016 qualifier against World Cup finalists Germany, who created one of the greatest sensations in the history of international football last night when beating Brazil 7-1.
Teemu Pukki was on target three times for Celtic against Linzer in Austria, where they face a further match against Dukla Prague on Friday before returning home, but the condition of his captain will have been at the forefront of manager Ronny Deila's mind.
Brown was sent to hospital for a scan after being stretchered off against Rapid on Sunday.
But Deila admits Brown could be sidelined for as long as three months - ruling him out of the opening two group games.
"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."