Dunbar, who missed the World Cup through injury, appears to have aggravated a problem which caused him trouble earlier in the season.
Glasgow coach Gregor Townsend said: “He missed three weeks with a groin/hamstring strain and he felt something twinge there. It was the same hamstring. He was over the ball and he felt it tighten. He doesn’t think it is as bad as the last time.”
Scotland kick off their Six Nations campaign at home to England on 6 February.