Friday against Phoenix, Leonard would suffer a partial tear to his left shoulder.
This setback adds to Kawhi's frustrations this year after he missed the first 27 games of the campaign.
The Spurs have two more games on their current road trip as they'll take on the Sacramento Kings on Monday and the Los Angeles Lakers on Thursday.
"It's too bad", Popovich said, per Tom Orsborn of the San Antonio Express-News. "It depends on how his shoulder goes". Popovich did not rule Leonard out for either game on Sunday, although Spurs guard Manu Ginobili told the media that, "We lose him for a few games, and we don't for how many, so it's been a tough season". "He was starting to get back into form a little bit after playing a couple of games".
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Leonard has only played in eight games this season, having returned on December 12 but having been held out of four of the Spurs' past 10 games, as the team has tried to manage his recovery. He has played in 39 games this season and notched a triple-double earlier this year.
"The first priority right now is making sure everyone is healthy and make sure that we are healthy at the crucial part of the season, going into the playoffs", guard Patty Mills said.
Since then he has been on a minutes restriction and rested regularly since returning, in true Gregg Popovich fashion, but Leonard has been fairly productive (15.9 points, 4.3 rebounds, 2.1 assists and 1.8 steals per game over just under 23 minutes per game).
Kyle Anderson should continue to get the start at small forward while Leonard is on the shelf.