Conley was diagnosed with a transverse process fracture in his back and will be reevaluated before New Year's Day.
The injury occurred in the third quarter of Monday's loss to the Charlotte Hornets, and continues a painful theme for the Grizzlies this season.
Conley is averaging career-best 19.2 points, 5.7 assists and has played all 82 regular-season games just once since entering the league at age 20 in 2007.
He missed 26 games last season due to a left Achilles injury.
Conley, who re-signed as an unrestricted free agent in July on the richest deal in NBA history - six year, $153 million -- will be in street clothes alongside another key free agent, forward Chandler Parsons. Parsons is dealing with a knee injury.
Longtime Grizzlies power forward Zach Randolph has missed the past three games grieving the death of his mother.
Former Kentucky point guard Andrew Harrison, who spent last season in the D-League, and 2016 first-round pick Wade Baldwin, are the short-term candidates to fill Conley's void.
Memphis, 11-7 this season, entered Tuesday in fifth place in the Western Conference.