Clippers coach Doc Rivers also said guard Patrick Beverley will sit out with a sore right groin.
Leonard typically sits out the second game of back-to-backs. He scored 26 points in a 134-109 win over the San Antonio Spurs on Saturday night. He is averaging 25.5 points, 7.8 rebounds and 5.1 assists per game.
Leonard's absence will put more responsibility on forward Paul George, who will play his first game in Oklahoma City since being traded in the offseason. George finished third in the MVP balloting last season with the Thunder.