The club recalled Dan LaCosta from its American Hockey League affiliate in Syracuse on Monday to fill in for Leclaire.
Fredrik Norrena will start for the Blue Jackets when they host Calgary on Tuesday night.
LaCosta has a 7-2-3 record with a 2.16 goals-against average at Syracuse this season. He was the Blue Jackets' third pick and 93rd overall in the 2004 draft.
Leclaire is 24-15-6 this season and leads the NHL with nine shutouts.