Andrew Taylor was forced off after 42 minutes of Saturday's 1-1 draw against Crystal Palace.
Strachan admitted that Gary O'Neil and Rhys Williams were also struggling and he may be forced into calling up players from the youth team at Home Park.
Emanuel Pogatetz's (knee) availability remains unclear, but Jeremie Aliadiere (broken toe), Willo Flood (knee), Seb Hines (ankle and medial ligament), Tony McMahon (stress fracture of the foot) and Matthew Bates (cruciate ligament) are all out.
But there was at least some positive news for Strachan as Scott McDonald made a goalscoring return to action at the weekend following his recovery from a hamstring injury.
Jay O'Shea came off the bench to make his debut against the Eagles and will be pushing for a starting berth.