Scans in Sydney Monday revealed the 27-year-old's knee would need reconstruction, the Waratahs said in a statement.
Palu, who had only just re-signed with the Australian Rugby Union and the Waratahs through 2012, had to be helped off the field after falling awkwardly in a tackle in the second half of their 20-13 loss in Christchurch.
The third-placed Waratahs also have other injury worries with prop Benn Robinson suffering a small fracture in his forearm and hooker Tatafu Polota-Nau sustaining slight ligament damage to his right shoulder.
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The Waratahs have a bye week and next play on April 24 when they host the ACT Brumbies in Sydney.
"It's going to be a bit of a waiting game with both Robbo and Tatafu," Waratahs coach Chris Hickey said.
"They both have fairly significant injuries and if we didn't have the bye this week they definitely wouldn't be available.
"In that sense, the injuries have come at a good time."
