The 30-year-old suffered the injury in Friday's game versus the Los Angeles Clippers.
Wall, who has suffered several injuries in recent seasons, has been limited again during his first campaign in Houston. He missed five games in March due to a knee contusion, and also sat a handful of contests in January with soreness. Both ailments involved his left knee.
After missing another four games earlier this month, the five-time All-Star revealed he's also battling hamstring tightness and a hip contusion.
"(Knee inflammation has) been there almost since I got hit in the Lakers game early in the year," he told the Houston Chronicle's Jonathan Feigen after returning against the Dallas Mavericks on April 7. "But it's not really bothering me. I can play through that. It was more so the tightness in my hamstring and my hip contusion that was bothering me."
He averaged 20.6 points, 6.9 assists, 3.2 rebounds, and 1.1 steals per game across 40 starts this season.