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The 25-year-old has since gone under the knife in London to mend his cartilage with no time being given as to how long he will be forced to sit on the sidelines for.
Wales travel to South Africa this summer, with the first Test on June 14, but Ospreys medical performance manager Towers isn't being drawn on a length of recovery.
He said: "Rhys had a scan on Monday which excluded any signs of ligament damage. However, he has gone to London for keyhole surgery to deal with a cartilage problem.
"Following discussions with the surgeon post-operation, we will be in a better position to discuss any potential return to play date."