Tahu suffered the injury during Australia's 38-28 loss to New Zealand on Saturday. He joins injured forward Willie Mason who hurt his AC joint during the Kangaroos Invitational match against New Zealand A.
The Kangaroos have not yet named a replacement for Tahu for the series which also features Great Britain.
Meanwhile, New Zealand's three-try hero Clinton Toopi is in doubt for Friday's second rugby league Tri Nations Test against Australia in Auckland.
Centre Toopi is battling to overcome a knee injury sustained in Saturday's shock 38-28 win over the Kangaroos at Telstra Stadium in which he crossed for hat-trick of tries. Coach Brian McLennan is waiting for the results of MRI scans on the knee for a clearer picture on his availability.
Hooker Lance Hohaia has already been ruled out the Kiwis team for the Ericsson Stadium return match after suffering a leg injury on Saturday night.