Rees is set to be out for two weeks, which would also mean him missing the Millennium Stadium appointment with Scotland on Sunday week.
The former Wales captain is in a battle for the number two shirt with Huw Bennett, with the latter set to win his 50th cap in Dublin.
Rees' absence now means a probable place on the bench for his Scarlets team-mate Ken Owens, who made his Test debut during the World Cup in New Zealand.
The injury to Rees is the latest blow to Wales, with fitness doubts remaining over centre Jamie Roberts, fly-half Rhys Priestland and flanker Dan Lydiate.
Wales coach Warren Gatland has already lost prop Gethin Jenkins and his World Cup locks Luke Charteris and Alun-Wyn Jones due to injuries as they prepare for a World Cup quarter-final rematch against Ireland at the Aviva Stadium.
Gatland will announce his team on Friday.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.