The Glasgow Warriors lock, who is departing Scotstoun after eight years to join Exeter Chiefs in the summer, has played in Scotland's defeats in Ireland and at home to England in the Calcutta Cup clash.
The BBC reports that the 25-year-old forward will sit out the rest of the campaign through injury.
Gray has been partnered by Glasgow team-mate Scott Cummings in the second-row for both matches so far, but head coach Gregor Townsend could call on experienced Edinburgh duo Grant Gilchrist and Ben Toolis to replace the 55-cap Warriors man, while Alex Craig is another option.
Scotland's remaining fixtures see them travel to Italy on February 22 before a home clash with France on March 8. Their tournament finishes with a trip to Wales on March 14.