Brown has a thigh injury and will be joined on the sidelines for the match in Turin next Wednesday by defender Mikael Lustig who has bone bruising.
Celtic's hopes of reaching the quarter-finals are hanging by the slimmest of threads after they lost the first leg 3-0 in a physical encounter in Glasgow two weeks ago.
"We're still waiting to hear about Brown but he will miss Juventus and the Scotland double header," Lennon told reporters.
"We are still waiting to hear from the specialist, whether he requires surgery or not and I am hoping that we will get a definitive answer by the end of the week...
"Lustig is out for two to three weeks, it is bone bruising so it could even be longer.
"So I imagine he will miss Juventus.
"Kris (Commons) is back from his virus and Lassad (Nouioui) has had a bit of a virus but he is in the squad."
Scotland, who are bottom their 2014 World Cup qualifying group, play back-to-back Group A matches on March 22 and 26.
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- Mikael Lustig