Jokinen, the team's second-leading scorer with seven goals and 18 points, was injured in the first period Wednesday night at Columbus when he was checked hard into the boards by Blue Jackets defenseman Marc Methot.
Jokinen went to the bench apparently favoring his left shoulder, then went to the locker room for treatment and did not return to the game.
The Coyotes released no details of Jokinen's injury at Thursday's practice, but coach Wayne Greztky said Jokinen will miss Friday's home game against Colorado and "it looks like [he'll be sidelined] for two to four weeks."
Jokinen, acquired in a trade with Florida in June, last missed a game during the 2002-03 season while with the Panthers.
Meanwhile Thursday, forward Daniel Winnik was taken off the injured reserve list and will play Friday after missing six games because of an upper-body injury.