Blue Jackets general manager Scott Howson announced the move on Tuesday.
Klesla was injured in a mid-ice collision with the Blues' Barret Jackman during the first period of the Blue Jackets' 5-2 victory Monday night. He is believed to have torn a groin muscle and is expected to be sidelined for at least a month.
Klesla lay on the ice for 5 minutes and did not put any weight on his left leg when he was helped off.
Columbus brought up defenseman Mathieu Roy from the team's AHL affiliate in Syracuse to replace Klesla.