Forward Cooper Marody has also been assigned to the Bakersfield Condors of the AHL.
Klefbom left Tuesday’s game against the Colorado Avalanche after blocking a shot from Sven Andrighetto. After the game, head coach Ken Hitchcock said Klefbom will be out “weeks not days” with the injury.
The 25-year-old Klefbom leads all Oilers players with 25:25 of ice time per game. He has three goals and 15 points in 31 games this season.
Caggiula, 24, missed four games with a hand injury. In 23 contests this season, he has seven goals and 10 points.
Marody has appeared in six games for the Oilers this season and has yet to record a point. In 11 AHL games, he has four goals and 14 points.
The Oilers have also recalled defenceman Caleb Jones from AHL Bakersfield.
The 21-year-old leads all Condors with 12 points in 21 games.