Brown has been struggling despite undergoing surgery this summer
Scott Brown could miss Celtic's Europa League encounter with Hamburg and Scotland's friendly against Wales.
The midfielder faces an extended spell on the sidelines in a bid to overcome his lingering ankle injury.
Brown sat out Celtic's league win away to Hamilton on Sunday and will not play in Wednesday's Co-operative Insurance Cup quarter-final against Hearts.
Celtic assistant Mark Venus said: "I think he's got a problem and he needs a rest. It's well-documented."
Venus expects Brown to miss Saturday's Scottish Premier League meeting with Kilmarnock and expressed a desire for Brown not to return until he is fully fit.
"For Scotland, for Celtic, for everyone, for the kid, for his performances, I think he has got to get himself fit properly," he said.
Hopefully, he will take as long as it takes to come out on the pitch next time as the proper Scott Brown
Celtic assistant manager Mark Venus
"I haven't seen him for a couple of days," said Venus. "I do know his ankle is very sore.
"I would suggest he isn't fit for selection this weekend either. After that, I'm not sure."
The 24-year-old Brown underwent surgery on his ankle in the close season and missed the first few games of Tony Mowbray's reign.
However, he has struggled to shake off the pain in his ankle and visited a specialist in London earlier this month before pulling out of Scotland's friendly in Japan.
Celtic face Hamburg in the Europa League on Bonfire Night and visit Falkirk in the SPL three days later.
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