The 23 year-old sustained ligament damage to his thumb during the club's 9-3 loss to Ulster at Murrayfield Stadium last Friday in what was his 20th start in as many appearances for the side this season.
Following specialist consultation at the Spire Hospital in Leeds, Fife had corrective surgery on his hand yesterday (Monday) and is expected to be out of action for the next two months.
Head coach Alan Solomons said: "This is really disappointing news for Dougie [Fife] and the club."
"He has developed and performed well for us this season, which culminated in his first Scotland cap in the recent RBS 6 Nations, so it's a pity that his best season of senior rugby has been brought to a premature end."
"However, as always at times of player injury, it presents others with opportunities to play and promote themselves into contention for regular selection."
The club also confirmed that top try scorer Tim Visser - absent with a broken leg and ankle ligament damage since October - has begun light training with the squad and is expected to return next month.
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