Chandler and Ellis were injured in the first four minutes of the game.
Chandler was injured less than a minute into the game when he was fouled by Clippers center Spencer Hawes. Ellis left the game three minutes later after suffering a left hip injury.
The Mavericks play the Utah Jazz on Wednesday, their last game before the All-Star Break.
Without Chandler in the lineup, the Mavericks were dominated on the glass by Clippers center DeAndre Jordan, who pulled down a career-high 27 rebounds to go with 22 points.
"It’s nothing we can control right now" Mavericks forward Dirk Nowitzki said to The Dallas Morning News. "We don’t expect either to play on Wednesday and we have to be better with what we’ve got. We have to be better defensively. We’ve got to somehow find ways to have five guys in there rebounding. That’s what it comes down to."
The Mavericks are already without point guard Rajon Rondo, who is sidelined with an orbital bone fracture.
Ellis is the Mavericks leading scorer at 20 points per game and Chandler leads Dallas in rebounding this season.
Dallas (35-19) is fifth in the Western Conference standings, one game behind the Portland Trail Blazers.
- Scooby Axson