San Antonio veterans Tim Duncan and Manu Ginobili will both sit out the second game of a back-to-back for rest.
Duncan had 20 points and 15 rebounds and Ginobili added 10 points and seven assists in the Spurs' 109-100 victory over the Dallas Mavericks on Thursday. Patty Mills had 26 points and six assists starting in place of Parker.
The victory pulled San Antonio (61-18) within a game of clinching the top seed in the Western Conference and moved Phoenix percentage points ahead of Dallas for seventh place.
The Suns (47-31) have won nine of 11 to surge back into the playoff picture after dropping three straight in mid-March.
The Spurs lost to Minnesota on Tuesday to split their games in Parker's absence.
The All-Star guard left San Antonio's 112-92 home victory over Memphis late in the first quarter Sunday after taking a hard fall as he drove the lane. After landing squarely on his back near the free throw line, he played for another 5 minutes before exiting with 2:41 remaining in the opening quarter.
Parker leads the team in both scoring (16.8 points) and minutes played (29.7) this season.