Frederic (upper body) will not return to Monday's game against the Lightning.
Bleackley wasn't given a qualifying offer from the Blues, making him a free agent, Jim Thomas of The St. Louis Post-Dispatch reports.
Bleackley was reassigned to AHL Chicago on Saturday.
Bleackley signed a three-year entry-level contract with the Blues.
Bleackley will be eligible to reenter the 2016 NHL Draft, NHL.com reports.
Bleackley was acquired by the Coyotes from Colorado on Monday along with Alex Tanguay and fellow prospect Kyle Wood in the deal for Mikkel Boedker, Renaud Lavoie of TVA Sports reports.