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The former British and Irish Lions captain, who has been dogged by injury in recent years, has only played two games for Munster this season and the back injury also forced him to sit out Ireland's November internationals.
Munster said in a statement that the 33-year-old lock would undergo back surgery at the earliest opportunity but did not give a time frame for how long his recovery would take.
Ulster wing Tommy Bowe, the country's third highest try scorer of all time, was ruled out of the Six Nations earlier this month with a knee injury. Ireland open their campaign in Wales on February 2.