Low and Ruaridh Jackson sustained injuries during the first-half of Glasgow Warriors' RaboDirect PRO12 match away to Scarlets on Saturday.
Stand-off Jackson, 23, was withdrawn with a leg injury when kicking an early penalty but no long-term issues are anticipated.
However, Low, 27, has since been assessed by orthopaedic surgeon Graham Lawson at Spire Murrayfield Hospital, who confirmed that the prop has suffered damage to the medial collateral ligament.
While it is common for this injury to require re-evaluation the expectation is that Low will be absent for at least eight weeks.
Warriors head coach Sean Lineen said: "This is clearly very disappointing news for Moray.
"He's an ambitious player who is extremely keen to achieve success with both Glasgow and Scotland, and the injury has come at a very unfortunate time.
"He's a tough character, however, and I know he'll work hard to bounce back strongly.
"In terms of his rehab, he'll be in great hands with the medical and physio team we have here at the Warriors."
Jackson's prognosis was more encouraging although he is expected to miss Glasgow's Heineken Cup Pool Three clash with Leinster at Firhill this weekend.
A Warriors spokesman said: "Ruaridh has reacted well to treatment since Saturday's game and the Warriors medical team are happy with his progress.
"He will continue to be monitored closely in the lead-in to our Heineken Cup matches and, from Scotland's perspective, for the RBS 6 Nations Championship."
Scotland head coach Andy Robinson said: "We all wish Moray a speedy recovery.
"As far as Ruaridh is concerned we will be monitoring his progress closely before the players come into camp with us later this month."
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