The New Zealand-born 29-year-old suffered the injury during his country's recent victory over South Africa and was subsequently ruled out of the triumph over Georgia last weekend.
Payne will also play no part when Ireland attempt to make it three wins out of three this month against the Wallabies.
There is more positive news of hooker Rory Best, who missed the victories over the Springboks and Georgia due to a calf strain.
Ireland forwards coach Simon Easterby said on Tuesday: "He (Best) trained today and trained well.
"I suppose we have three very good hookers available to us now. It’s a position of real strength, with Straussy (Richardt Strauss) going really well at the weekend against Georgia and Sean (Cronin) doing particularly well against South Africa.
"It's a good place to be. Rory has proved his fitness today and took part in full training, which was great. It's great to have a bit of quality and depth in that position."
Mike McCarthy will miss out against Australia as the lock has returned to Leinster to undergo return-to-play protocols after suffering concussion against Georgia.
Chris Henry is also sidelined due to a blocked blood vessel in his brain which forced him to withdraw from the side that beat South Africa.