Farmar received an ultrasound and was examined by Dr. Luga Podesta on Tuesday after suffering the strain during practice Monday. Farmar also underwent platelet-rich plasma therapy for the injury.
Farmar has already missed 30 games this season because of two separate tears to his right hamstring.
The 27-year old is averaging 10.4 points, 4.7 assists and 2.5 rebounds per game while shooting 45.7 percent from 3-point range. He is one of 11 players on the Lakers' 15-man roster set to become a free agent this summer, with Nick Young (player option) potentially being the 12th.
"They'll all probably play together, so they have to be able to rely on each other to bring it up (based on) which one has less pressure and make plays," D'Antoni said. "Obviously you just got to move the ball and go through Pau [Gasol] more. Pau probably needs to be on the floor more with those guys to make plays."
Steve Nash, who was initially ruled out for the rest of the season by D'Antoni last week because of persistent nerve root irritation in his back and hamstrings, could also return to the lineup. But that possibility is remote.
"We'll see," D'Antoni said. "He hasn't practiced with us, so that would be a stretch."
The Lakers are hoping to welcome back two other injured players this week, however. Young, out since Feb. 23 with a non-displaced fracture in his left knee and Jordan Hill, out since Feb. 28 with a sore right knee, both practiced for the second consecutive day Tuesday. D'Antoni said that Young was closer to game action than Hill was, but that both could return by the weekend.