Frye was injured in Sunday's loss to Oklahoma City as the ninth-place Suns hope to claw their way into the post-season by finishing in the top eight in the Western Conference.
The Suns (32-29) are currently two games behind the Memphis Grizzlies for the eighth spot.
The 6-foot-11 (2.11m) Frye, who signed a five-year contract extension in the off-season to stay with Phoenix, is averaging a career high-tying 12.3 points and 6.6 rebounds a game.
He is fifth in the NBA in three-pointers made and will be a difficult player for Phoenix to replace.
"We spent about two hours talking about (who will play in his place) as a coaching staff this morning," Phoenix coach Alvin Gentry told the team's website (www.nba.com/suns).
"I'm sure we'll revisit it tomorrow some because there's a lot of ways that we can go."
(Reporting by Jahmal Corner in Los Angeles; Editing by Steve Ginsburg)