Phipps, who was forced from the field during the away loss against the Otago Highlanders last week, would be replaced by Jake Gordon in the Waratahs' starting 15, the team said in a media release on Thursday.
Phipps was named in Michael Cheika's Wallabies squad for tests against Fiji, Scotland and Italy, but his injury may open the door for uncapped ACT Brumbies scrumhalf Joe Powell to debut.
Veteran scrumhalf Will Genia is expected to be handed the starting number nine shirt against Fiji on June 10 at Melbourne Rectangular Stadium.
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The Daryl Gibson-coached Waratahs need to beat the Chiefs and then hope the Australian conference-leading Brumbies lose to the Melbourne Rebels to keep their razor-thin playoffs hopes alive.
(Reporting by Ian Ransom; Editing by Greg Stutchbury)
