Geldenhuys originally suffered the injury to his right knee while training with Jacques Brunel's Italy squad earlier this week.
And further scans on Friday revealed that the lock has suffered medial ligament damage, with the timeframe for recovery set at 45 days.
The 33-year-old, who has made 52 appearances for Italy during his career, has been replaced in the Azzurri squad by Treviso second-row Marco Fuser.
The South African-born forward has been a key figure for Zebre this term, playing in all but one of their GUINNESS PRO12 matches and notching his first try of the campaign against Treviso earlier this month.
But he is now set for a spell on the sidelines, with Zebre's trip to Ospreys on March 28 a likely target for his return.
"The Italy and Zebre second row Quintin Geldenhuys underwent a scan on the injury sustained in training in Rome on Tuesday morning with the national team," said a statement from the Italian national rugby federation (FIR).
"The tests have confirmed a second degree lesion of the medial collateral ligament in his right knee, with recovery time estimated at 45 days."
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