Clippers ace Leonard, who made an acrimonious departure from San Antonio in 2018, was subjected to loud booing as he lined up to take free throws near the end of the second quarter in San Antonio.
The heckling drew the ire of San Antonio's famously gruff veteran coach Popovich, who grabbed a courtside microphone to address the home fans directly.
"Excuse me for a second, please stop all the booing, let these guys play, and show a little class," Popovich barked.
"It's not who we are. Knock off the booing."
Popovich was reluctant to expand on the incident after the game, saying simply that he did not want Leonard to be motivated by his detractors in the stands.
"You don't poke the bear," Popovich said. "Anybody who knows anything about sports knows you don't poke the bear. That's my answer."
Leonard later brushed off the catcalls, saying it was to be expected.
"If I don't have a Spurs jersey on they're probably gonna boo me for the rest of my career," he told reporters after the game.
"It is what it is. They're one of the best fanbases in the league and they're competitive, and when I step on this basketball court I can hear that.
"When I'm on the streets or going into restaurants they show love."
Leonard launched his career with San Antonio after being traded to the Texas club immediately after being picked by Indiana with the 15th selection in the 2011 draft.
In 2014 he played a starring role in San Antonio's NBA Finals victory, being named Most Valuable Player in the 4-1 series victory over the Miami Heat.
His stay in San Antonio came to an unhappy end in 2018, however, when he demanded a trade from the club amid differences over how to manage his injury rehabilitation.
He subsequently joined the Toronto Raptors, leading them to his second NBA championship and Finals MVP in the 2018/19 season.