The knock has curtailed his involvement in the Scotland training camp at St Andrews but he is expected to be available for the Test match with New Zealand on November 11.
Scotland team doctor James Robson said: “Ryan Grant, the Glasgow Warriors prop, sustained a concussive episode against Treviso at the weekend and is currently subject to our graduated return to play protocol.”
Ryan's fellow Warriors - Alastair Kellock (back), Ruaridh Jackson (shoulder) and Sean Lamont (facial) - undertook limited training today.