The Blues sent prospect Maxim Letunov to Arizona in exchange for Michalek and a conditional third-round pick.
Michalek, 32, has blocked 130 shots and put up two goals and six assists in 53 games this season.
He is out with an upper-body injury but has said he's feeling better and could be back soon for St. Louis.
Michalek is a pending unrestricted free agent.
"We would like to thank Zbynek for all his contributions to the Coyotes over the years," Arizon general manager Don Maloney said in a statement. "'Z' is a fierce competitor and a great person and we wish him all the best in the future."
Letunov is a 19-year-old playing in the USHL who was the Blues' second-round pick in last year's draft.
"Maxim is a big, skilled center with excellent upside," Maloney said in a statement. "He will play at Boston University next season who do a great job developing players. We are excited to have him join our organization."