The 26-year-old only made the move to the Allianz Arena in the summer from FC Twente but found it tough to settle as Bayern struggled through the opening months of the season.
Team-mate and club captain Mark van Bommel admitted Braafheid has been unfortunate as his arrival coincided with the German giant's difficult spell.
Van Bommel told Bayern's official website: "He's been unlucky. When he played, the team as a whole wasn't playing well.
"You can't play to your potential in those circumstances. He's not been able to show what he can do."
The left-back will fill the void created in Mowbray's backline by Danny Fox's recent departure to Burnley.
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