The lock sustained the injury during the side's 28-18 loss to Wales yesterday and will undergo a scan to determine the extent of the damage tomorrow.
Scotland's team doctor James Robson told reporters: "Richie is due to be scanned at Spire Murrayfield hospital with a view to a more accurate assessment of the injury he sustained on Saturday.
"At this stage I can confirm he will play no further part in this year's championship. It would be premature to speculate further at the moment. We'll have a better understanding then of the degree of injury to the muscle.
"Richie is on crutches at present and is grateful for the good wishes from supporters."
Scotland face France in the final game of the tournament next Saturday.