The Lakers announced the backup point guard's injury Monday. The team also said Pau Gasol has a mildly sprained right ankle.
Farmar left Sunday night's game against Portland after playing just 56 seconds. He had an ultrasound examination Monday.
The 27-year-old guard announced on his Instagram account that he received platelet-rich plasma therapy on his hamstring shortly after the diagnosis.
"PRP done this afternoon," Farmar wrote in a caption for a photo of the back of his left leg being injected with a needle. "Healthy blood platelets put directly into the tear! I'll be back ASAP and better than ever! Our guys got heart and will keep fightin!"
Farmar is off to a strong start in his return to Los Angeles, where he won two NBA titles before playing for New Jersey and in Turkey. The UCLA product has averaged 9.2 points and 4.4 assists in 18 games.
Also Monday, the Lakers announced they had recalled D-Fenders forward Ryan Kelly. Kelly currently is ranked fifth in the D-League in scoring average and tied for seventh in minutes per game. He has appeared in two games for the Lakers this season.
ESPNLosAngeles.com's Dave McMenamin and The Associated Press contributed to this report.