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Glenn, 28, had been battling the injury late in the NRL season before having the operation on Wednesday.
He is expected to be back in time for next season for the Broncos.
"It is a three-to-four month recovery for an operation of this sort," Broncos high performance manager Jeremy Hickmans said.
"That means he would be available in the first few weeks of the trials, so he shouldn't miss any time from games there."
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Glenn, a veteran of 12 Tests for New Zealand, will miss the Four Nations, which start on October 28.
New Zealand will face England, Australia and Scotland.