In a statement, Juve said that Bremer, who missed most of last season with an anterior cruciate ligament injury, was diagnosed with the tear in Lyon on Monday morning.
"In the next few hours the player will undergo selective arthroscopic meniscectomy," Juve added.
Italian media report that the 28-year-old could be out for a month, with Juve facing high-flying Como in Italy's top flight on Sunday.
It is a further blow to coach Igor Tudor as Juve were already missing fellow defender Juan Cabal, who suffered a thigh injury during his team's 2-2 draw at Villarreal in the Champions League earlier this month.
Juventus are fifth in Serie A on 12 points and have drawn their last five matches in all competitions.