San Antonio hosts the Golden State Warriors on Monday down 3-0 in the Western Conference Finals.
Leonard was already considered doubtful to play after missing the previous two games with an ankle injury.
"If he's unable to play yesterday, I don't think there's going to be a miraculous healing by tomorrow," Spurs head coach Gregg Popovich said Sunday, per Melissa Rohlin of the San Antonio Express-News.
The 25-year-old initially hurt his ankle during the second round against the Houston Rockets, and he reaggravated the injury in Game 1 against the Warriors. After landing awkwardly on Zaza Pachulia, he was forced out of the game and hasn't appeared since.
San Antonio squandered a 23-point lead after Leonard left the game, costing the No. 2 seed a series-opening win. The team lost the next two contests by a combined 48 points.
Jonathon Simmons and Kyle Anderson will continue to earn playing time at the forward positions, but the Spurs will need a full team effort to extend the series at least another game.