The team said Parker underwent an MRI exam on Monday that revealed a sprained facet joint on his left side.
Parker will miss games against the Minnesota Timberwolves on Tuesday and the Dallas Mavericks on Thursday.
Parker left Sunday's 112-92 win over the Memphis Grizzlies in the first quarter with back spasms after playing nine minutes and scoring 10 points. He will be listed as day-to-day after the game against the Mavericks.
Parker is averaging 16.8 points, 5.8 assists and 2.3 rebounds in 65 games this season for the Spurs. San Antonio has a 4.5-game lead over the Oklahoma City on Thursday for the top spot in the Western Conference.