The Scotland internationalist suffered ligament damage to his thumb during the club's 9-3 defeat by Ulster and had an operation in Leeds on Monday.
The 23-year-old is expected to be out for two months. "This is really disappointing news for Dougie and the club," said Alan Solomons, the Edinburgh head coach. "He has developed and performed well for us this season. 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 promote themselves into contention for selection."
Solomons is expected to have Tim Visser back next month after the winger resumed light training following his leg break.