A decision has been made to call up Munster's Damien Varley to the squad and he is expected to arrive in New Zealand by Saturday.
Commenting on the injury to Flannery, Ireland team manager Paul McNaughton said: "Obviously it is particularly disappointing for Jerry to have suffered this injury at this point in the tournament.
"With the fact that he is out for four to six weeks, we needed to make the decision to fly Damien Varley down as soon as possible.
"Sean Cronin will step into the replacements seamlessly this weekend which shows the importance of having experience and depth in the squad."
IRELAND Team & Replacements (v Australia, 2011 Rugby World Cup Pool C, Eden Park, Saturday, September 17, kick-off 8.30pm local time/9.30am Irish time):
15 - Rob Kearney (UCD/Leinster) *
14 - Tommy Bowe (Ospreys)
13 - Brian O'Driscoll (UCD/Leinster) (capt)
12 - Gordon D'Arcy (Lansdowne/Leinster)
11 - Keith Earls (Young Munster/Munster)
10 - Jonathan Sexton (St. Mary's College/Leinster)
9 - Eoin Reddan (Lansdowne/Leinster)
1 - Cian Healy (Clontarf/Leinster) *
2 - Rory Best (Banbridge/Ulster)
3 - Mike Ross (Clontarf/Leinster)
4 - Donncha O'Callaghan (Cork Constitution/Munster)
5 - Paul O'Connell (Young Munster/Munster)
6 - Stephen Ferris (Dungannon/Ulster)
7 - Sean O'Brien (Clontarf/Leinster) *
8 - Jamie Heaslip (Naas/Leinster)
16 - Sean Cronin (Leinster) *
17 - Tom Court (Malone/Ulster)
18 - Donnacha Ryan (Shannon/Munster) *
19 - Denis Leamy (Cork Constitution/Munster)
20 - Conor Murray (Garryowen/Munster)
21 - Ronan O'Gara (Cork Constitution/Munster)
22 - Andrew Trimble (Ballymena/Ulster)
* Rugby World Cup debutant
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