Van der Merwe represented Canada at the recent Rugby World Cup, and as with all returning players, was subject to assessment by the Glasgow Warriors medical team.
With these checks having highlighted a suspected issue with the 25-year-old's shoulder, he was sent for further assessment by specialists at the Murrayfield Spire Hospital.
It has been confirmed that the injury requires surgery.
Warriors team doctor Gerry Haggerty said: "At this stage, it's very difficult to put an estimate on the likely recovery time, but clearly we will continue to monitor DTH closely.
"DTH will have the full support of the medical team at Scotstoun, and we look forward to assisting him in his recovery."
Head coach Sean Lineen said: "It's obviously disappointing that a quality player like DTH requires surgery, and everyone at the club wishes him all the best for the operation and his subsequent rehabilitation."
Van der Merwe has not been included in the Warriors' initial 38-man squad for the Heineken Cup ahead of the tournament launch.
Under competition rules, during the pool phase clubs can register up to two "additional players" as replacements for players registered in the initial squad.
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