The Frenchman joined Bayern from Galatasaray on January 28th as the German champions looked to boost their struggling defence.
"FC Bayern will be without Sacha Boey for the coming weeks after the 23-year-old January arrival suffered a large tear in his left hamstring in training," the club said in a statement.
The injury to the former France youth international could not have come at a worse time for Bayern, who are already without several injured players.
They have also lost their last two matches - a 3-0 league loss at Bayer Leverkusen last week and Wednesday's 1-0 defeat away to Lazio in their Champions League last-16 first leg.
Bayern, who visit VfL Bochum on Sunday, are in second place in the Bundesliga, five points behind leaders Leverkusen.
