It is another major blow for Farrell, who is still waiting to make his rugby union debut six months after completing a big-money cross-code switch to Saracens.
Farrell's union career has been on ice since August, when he broke a toe during a pre-season trial match that eventually required an operation.
The 30-year-old had returned to full training and was set to make his debut in Sunday's European Cup clash with Ulster before being involved in the road accident last week.
It is understood his car was shunted from behind.
Farrell pulled out of Sunday's match but Saracens director of rugby Steve Diamond had hoped he would be available in the "not too distant future".
But Farrell could now be ruled out until mid-March, casting doubt on whether he will feature at all for Saracens this season.
Diamond said only recently he expected Farrell to make a "huge impact" on rugby union once he recovers from a prolonged injury nightmare.
"We value Andy immensely," said Diamond.
"He is a proud man and a leader of men, so he's depressed by the situation. When he is fit, we're confident he will make a huge impact on rugby."
Farrell was a passenger in the car and initially the accident caused no distress.
But at the team's next training session on Thursday morning his back felt stiff in the warm-up. Subsequent scans diagnosed a prolapsed disc and it will require keyhole surgery.
Saracens chief executive Mark Sinderberry said: "It's terrible luck for Andy - particularly as this injury hasn't been picked on the rugby field.
"In a year in which Andy has suffered some very bad luck, this is a cruel blow to suffer such an injury away from the pitch - especially coming when he was nearing a return to full fitness. We wish him a speedy recovery."