The Munster lock, who captained Ireland in this season's RBS 6 Nations Championship while Brian O'Driscoll recovered from shoulder surgery, misses out due to a knee injury.
O'Connell had been undergoing rehabilitation in London this week in the hope that he could a join the squad, but the Irish Rugby Football Union said he had "failed to progress to the level required to allow him to take an active part in the tour".
Connacht's Mike McCarthy had already been added to the squad as cover while O'Connell continued his recovery programme.
Ireland will tackle the All Blacks in Auckland on June 9, followed by further Test matches in Christchurch and Hamilton on June 16 and 23.
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