Danny Nardiello, Chris Eagles, Rob Lainton, Kiel O'Brien, Marcus Poscha and Reece Brown will be released.
The Shakers, currently 15th in League One, have also activated a clause in captain Craig Jones' contract for a new one-year deal.
Bury have also offered reported Crewe target Ryan Lowe a one-year deal and are in discussions with midfielder Danny Pugh over an extension.
Bury have announced six players will be leaving Gigg Lane this summer.