He arrived in Queenstown on Monday but has not fully recovered from the injury in time for the eagerly-awaited tournament opener in New Plymouth.
"Cian won't be playing at the weekend. He won't resume contact work until the weekend, which was the original prognosis, so he won't be available for the USA game but will be available for the Australia game," explained team manager Paul McNaughton.
"He's been able to do a couple of scrums but not as much as normal."
McNaughton added: "Everybody else is fit and strong and available for selection, including Rob (Kearney), Sean (O'Brien) and Gordon D'Arcy."
Meanwhile, members of the Ireland squad will be present at Friday's launch of the New Plymouth Fanzone. The event will take place at Puke Ariki, Taranaki's combined museum and library, on the New Plymouth waterfront, starting at 7pm.
All official Rugby World Cup Fanzones are free to enter and are a great place to watch the match with other fans. Many Fanzones will also feature live entertainment before and after the games.
Follow the Ireland team in New Zealand on www.twitter.com/irfurugby.