During his two months with Blues, Bak made only five appearances, starting in three games and coming on as a substitute in two.
He has failed to produce the form that manager Bruce expected him to and his loan spell as been cut short by one month.
"Unfortunately Arek's time with Blues didn't work out, as both we and the player had hoped.
"However, we wish him every success in his future career," Bruce told the club's official website.