Farrell was withdrawn from Saracens' home European Champions Cup match against Glasgow on Saturday to have a minor procedure on his thumb, with the club's director of rugby Mark McCall saying the recovery period will be seven to 10 days.
Fly-half Farrell, a lynchpin in England's Championship push and captain for the trip to Dublin in the absence of the injured Dylan Hartley, is expected to travel to Portugal for their pre-tournament camp next week.
Yet his absence from training sessions will be a blow to England coach Eddie Jones' preparations for the Ireland game on Feb. 2.
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McCall told BT Sport that 27-year-old Farrell's problem was "minor" and he would be ready for a match which could go a long way to deciding the destination of the 2019 Six Nations.
There has also been a question mark over the fitness of Johnny Sexton, Farrell's Ireland counterpart who has been troubled by a knee tendon problem and will miss Leinster's final Champions Cup pool match at Wasps on Sunday.
Ireland coach Joe Schmidt said in naming his squad this week that the world player of the year was making "good progress."
(Reporting by Ian Chadband; editing by Ken Ferris)
