Farmar suffered the injury in Tuesday's loss to the Milwaukee Bucks, exiting the game early after feeling tightness in his left leg.
The 27-year-old Farmar underwent an MRI exam Wednesday morning and the tear was diagnosed.
Farmar previously suffered a tear in the same hamstring Dec. 1 and missed 10 games. The Lakers said the new tear is in a different location than the previous injury.
Farmar is averaging 8.7 points and 4.7 assists in 22 games this season.
The Lakers completed Tuesday's game with Kendall Marshall as the only healthy point guard on the roster.
ESPNLosAngeles.com's Dave McMenamin contributed to this report.