Leonard was ruled out of Saturday night's game against the Atlanta Hawks due to a left knee contusion. It was his second straight missed game after he also sat out the tail end of a back-to-back set Thursday due to left knee injury management.
Patrick Beverley, who has a sore left calf, also missed Saturday's game, which the Clippers won 150-101 behind George's 37 points.
Clippers coach Doc Rivers said Leonard suffered the left knee contusion Wednesday during the Clippers' 102-93 loss at Houston. Leonard is considered day-to-day, Rivers said, adding that there was "no concern" that it could be longer than that.
George made his season debut Thursday night in New Orleans and had 33 points and nine rebounds in 24 minutes during a 132-127 loss to the Pelicans.
The Clippers were hoping Saturday's game could be their first glimpse of Leonard and George playing together after the Clippers signed Leonard in free agency and traded five first-round picks, the rights to swap two first-round picks and Shai Gilgeous-Alexander and Danilo Gallinari for George.
The Clippers, who entered Saturday on a two-game slide, have been riddled by injuries of late. Shooting guard Landry Shamet will miss his third straight game with a high ankle sprain, while Beverley will miss his second straight.
"There's no way we can have continuity right now," Rivers said of the Clippers, who play Oklahoma City next when Gilgeous-Alexander and Gallinari return on Monday. "We've had one live practice with Pat, Kawhi, Sham, Paul George on the floor. One. This season. I'm talking training camp as well. So you're not going to have any continuity right now."