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O'Connell who captained the Lions during their last tour in South Africa four years ago, has played only two games for his provincial side Munster this season and last started for Ireland during last year's Six Nations.
The 33-year-old lock, who has been dogged by injury in recent years, underwent surgery on his back for the second time on Monday (local time) and said the operation had gone well.
"My aim now is to start rehab as soon as is practicable. In terms of a return, I'd be looking at early April," O'Connell told Munster's website on Tuesday.
Tommy Bowe has also been ruled out of the Six Nations championship, which Ireland begin in Wales on February 2, because of a knee injury. However, the Ulster wing should also return in April in time for possible inclusion in Lions' coach Warren Gatland's squad for Australia.