Ginobili strained a hamstring early in a win over the Clippers on Friday. Popovich said he didn't know how long Ginobili would be out, indicating it could be until the playoffs.
"It's more than days (until he returns), it's more like weeks, unfortunately," Popovich said. "It's a huge blow for us."
Before the Spurs last faced the Heat in November, Popovich, citing a desire to rest his best players at the end of a long road trip, sent Ginobili, Tim Duncan, Tony Parker and Danny Green home before a 105-100 loss at Miami, resulting in a $250,000 fine.
The Heat also were short-handed Sunday night.
Hours before tip-off, they announced that forward LeBron James (hamstring), guard Dwyane Wade (ankle) and guard Mario Chalmers (ankle) would sit out Sunday night's game, which resulted in a 88-86 Miami win.
Was sitting James and Wade a calculated response from the Heat for what the Spurs did in November?
"I could see how you guys can draw that conclusion, but no," Miami coach Erik Spoelstra said.
Information from ESPN.com's Tom Haberstroh and The Associated Press was used in this report.