Sale forward Gray, who was winning his 26th cap, was injured during the first half against the Springboks.
Scotland doctor James Robson said: "Richie will now be subject to the return to play protocol following a concussive episode. We have been in contact with his club medical team at Sale Sharks to discuss the management of his injury."
Scotland reported no other injury concerns following the defeat to the Springboks as they prepare for next Saturday's game against Tonga in Aberdeen.
Robson added: "Alasdair Strokosch is continuing his rehabilitation with us following the calf strain he sustained in training last week."
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