The lock has undergone surgery and is expected to be out for six to eight weeks after sustaining ligament damage around his thumb during last weekend's URC victory at home to Sharks.
Danny Wilson, the Glasgow coach, told The Scotsman: "For Scott, for Glasgow and for Scotland it's a blow that he'll be out for a period of time. But that's the game. It's a short-term injury really, but long enough that it will have an impact.
"It's unfortunate because I thought he was playing well, getting back to some really good form. He's had surgery and starts the recovery process now so he'll work hard to get himself back."