Steve Blake will start in Nash's place.
Nash played just two minutes in the Lakers' win over Sacramento on Saturday and missed most of the second half of L.A.'s loss to Milwaukee on Thursday because of the injury.
Nash said Tuesday he is optimistic about returning to action soon, possibly for Friday's game.
"You never know, but I'm definitely optimistic," Nash said. "It's getting a little better every day, but there's no guarantee."
The Lakers have a light schedule this week, however, and coach Mike D'Antoni was optimistic his point guard would return soon.
"I think he has a chance for Friday," D'Antoni said after shootaround Tuesday, looking ahead to his team's game against the Memphis Grizzlies. "So we'll see how it goes the next couple, three days and try to get him ready for Friday, if not 100 percent. That's our plan."
Blake had 15 points on 5-of-9 shooting, two rebounds and one assist filling in for Nash, and played 32 minutes against Sacramento.
Nash missed 24 of the Lakers' first 26 games after fracturing the fibula in his left leg Oct. 31. He had played in 48 straight games entering Tuesday.
"Every day he gets a little bit better, but he's just not quite ready to go yet," D'Antoni said of Nash, who did not practice Monday. "His hamstrings are still strained and he feels something, so until he doesn't feel anything, he can't play."
Injuries have been an ongoing challenge this season for the Lakers (38-36), who stand a half-game behind the Utah Jazz for the eighth and final playoff spot.
The Lakers have a 1½-game lead on the Mavericks, who beat the Lakers at L.A. in the season opener for both teams.
The Mavs have won four of their past five games; the Lakers have lost four of their past six.
Information from ESPNLosAngeles.com's Ramona Shelburne was used in this report.