O'Connell was thought to be making good progress in his recovery from a shoulder injury sustained in the 43-31 defeat by France in Paris earlier this month.
However, Ireland team doctor Gary O'Driscoll said the shoulder reacted adversely to the next level of training and the player was immediately ruled out of the Welsh game.
Ireland are confident, however, that O'Connell will be back in time for the home game against Scotland on Saturday, March 11.
"Based on Paul's reaction in training today (Tuesday), we repeated the scan which revealed that the shoulder has not healed to the extent we had anticipated," said O'Driscoll.
"Paul will continue with his rehabilitation and we are confident that he will be available for the Scotland game."
In the absence of his first-choice second rower, Ireland coach Eddie O'Sullivan is likely to pair the experienced Malcolm O'Kelly with Donncha O'Callaghan, although Mick O'Driscoll will also come under consideration.
Apart from the imperious O'Connell, O'Driscoll has been the next most impressive lock in Irish rugby so far this season.
Another Lions player, Saracens hooker Shane Byrne, has been added to the Ireland squad as precautionary cover for Jerry Flannery, who suffered an ankle strain in training.