Parker had been sidelined with stiffness in his lower back but played in Sunday's All-Star Game, finishing with four points, two rebounds and one assist.
"He doesn't have a pulled hamstring or anything, but he's got a lot of little things," Popovich said.
The Spurs have been mainstays in the playoffs throughout Parker's career, and he has also played with the French national team in the offseason. Popovich is concerned about the cumulative effect it's had on Parker.
"Basically a lot of basketball the last three years, all season long, all summer long," Popovich said. "It's caught up to him."
Parker did not cite specific injuries but said he agreed with the decision.
"The main thing with Pop, he doesn't want me to play 50 percent, 60 percent," Parker said. "That's the main thing. He wants me to get all of my little stuff healed. So however much time it takes, next time I come back on the court he wants me to be 100 percent.
"Against Charlotte, against Detroit, I was not myself. He just doesn't want me to play like that."
Spurs guard Manu Ginobili said he noticed Parker's recent struggles.
"I saw him struggling the last week before the break, aching and limping," Ginobili said. "I guess it's the right decision. Of course, we're not going far without him."