The Warriors have suffered a double blow with DTH van der Merwe sidelined for six weeks with a hamstring injury.
Glasgow's medical team released the medical updates on Monday after both players were taken off injured during Friday's RaboDirect Pro12 win over Zebre at Scotstoun.
Low has sustained medial ligament damage and will be out for eight to 10 weeks, but does not require surgery.
Low was called up for the final two games of Scotland's successful Australasia tour in the summer after being left out of the initial squad.
Head coach Gregor Townsend told the club website: "DTH and Moray are both important players for us, so it's clearly disappointing to have them unavailable over the next few weeks.
"The news isn't as bad as it could have been, though, and I know both guys will be working extremely hard under the care of our medical team to return to the field and continue making a significant contribution to our season."
- DTH van der Merwe