Parker injured the ankle late in the third quarter while landing after completing a reverse layup. Parker had to be helped off the court and did not return to the game.
Parker underwent an MRI on Saturday morning in San Antonio and the injury was revealed.
San Antonio holds a three-game lead over the Oklahoma City Thunder for the No. 1 seed in the Western Conference.
If Parker is out of action for the entire four weeks, he will miss key games against Oklahoma City, the Los Angeles Clippers and the Miami Heat.
After Friday night's game, Spurs head coach Gregg Popovich new the injury was very serious to his All-Star point guard.
"He'll be out a while," Popovich told the San Antonio Express-News. "It's a good one. Tony's been pretty stalwart for us. He's having an All-Star season, and as I said, I think playing better than any other point guard in the league consistently throughout the year. We'll definitely miss him."
Parker has been arguably the best point guard in the NBA this season. Parker is averaging 21.0 points and 7.6 assists per game, the second-highest season averages of his career in both categories, while leading the Spurs to an NBA-best 46-14 record.