Farah suffered the injury in the Tigers' controversial golden point 23-22 loss to Canterbury on Friday night.
And following X-rays on Saturday the club revealed in a statement Farah has a fractured right hand.
"An X-ray this morning showed Farah has a fracture, he then underwent a CT scan with the club expecting the results on Monday," the statement read.
With just two rounds of the regular season remaining, Farah's season appears all but over, leaving the Tigers' finals hopes in tatters.
The loss on Friday leaves Tim Sheens' men in eighth spot but they could be leapfrogged if Newcastle beat Manly at Brookvale on Sunday.
Tigers playmaker Benji Marshall praised his side for a massive effort in taking the competition leaders to extra-time.
The joint venture were on the end of some harsh calls by officials with the biggest talking point the baffling decision by video referee Sean Hampstead to award a try in the 74th minute to Bulldogs winger Jonathan Wright.
In the lead up to the try, back-rower Frank Pritchard ran behind Josh Morris, who impeded Tigers centre Blake Ayshford, before passing to Ben Barba who found an unmarked Wright.
But Marshall was too proud of his side's effort, after fighting back from 12-0 early to send to the game into golden point with a try to Aaron Woods in the 78th minute, to worry about refereeing.
"That's rugby league. It could have gone either way but at the end of the day they won fair and square. We had our chances to win it but we couldn't," Marshall said.
"If (Wright's try) went the other way they probably would have blown up about it as well. At the end of the day, that's the refs' call, they make that call and we can't control that.
"It was a big effort from the boys ... the character we showed in the second half to come back was great."
The Tigers play the Sydney Roosters at Allianz Stadium next round and Marshall said it was a danger game against a side who beat them 42-28 in June.
"I think it's good that we've got a long week until we play next weekend. We need a bit of recovery, a few of the boys are battered and bruised," Marshall said.