The defenseman was acquired by the Blues from the Montreal Canadiens on Tuesday for a second-round pick in the 2020 NHL Draft and a conditional fourth-round pick in 2021.
Scandella, who has 12 points (four goals, eight assists) in 51 games with the Canadiens and Buffalo Sabres this season, will be paired with Colton Parayko.
St. Louis, which ended a five-game winless streak (0-3-2) with a 3-0 win against the New Jersey Devils on Tuesday, is tied with the Dallas Stars for first in the Central Division.
The Coyotes, who lost 3-2 to the Stars on Wednesday, are tied with the Calgary Flames for the first wild card into the Stanley Cup Playoffs from the Western Conference and trail the Edmonton Oilers by three points for first in the Pacific Division.
Goalie Antti Raanta is expected to start for Arizona, which is 4-7-3 in its past 14 games.