The 33-year-old will not play a part in the Ospreys' next three games but they hope to have him back for the PRO14 match against Cardiff Blues at the end of April.
"Alun Wyn suffered knee ligament damage last weekend and is currently rehabbing," the Ospreys said in a statement.
"He won't travel to South Africa with the squad at the start of April (for games against Cheetahs and Southern Kings) but at this stage we haven't ruled him out of the Judgment Day game against Cardiff Blues."
The Ospreys also confirmed wing George North fractured two metacarpals in his left hand in the final match which ruled him out of the next set of fixtures.
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(Reporting by Rohith Nair in Bengaluru; editing by Sudipto Ganguly)
