Gray, who partners his brother Jonny in the second row, sustained tendon damage during Sunday's 26-23 defeat by Wales at Murrayfield and is expected to be out of action for around three months.
Glasgow Warriors lock Tim Swinson has been called into the Scottish squad for the rest of the tournament.
Scotland, who lost their first two Six Nations games, next host Italy on Feb. 28.
(Reporting by Ed Osmond; editing by Sudipto Ganguly)
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