Lock forward O'Connell, 35, had said before the World Cup that he would retire from international rugby at the end of the tournament, but his departure has been enforced earlier than planned by the hamstring injury sustained during Sunday's 24-9 pool victory over France.
"Paul O'Connell suffered a significant hamstring injury and will undergo surgery this week," the IRFU said in a statement. "Paul will not play again at Rugby World Cup 2015 and his time out of the game will depend on the outcome of the surgery."
Mike McCarthy has been called into the squad as a replacement ahead of Ireland's quarter-final against Argentina in Cardiff on Sunday.
"It's been amazing to play with him," Ireland prop Jack McGrath told reporters. "He was a true warrior. He never left anything out there on the pitch."
Young Ireland centre Robbie Henshaw also paid tribute to O'Connell's influence.
"He was always there to give me advice when I came into the squad," Henshaw said.
"I loved and admired the fact he wasn't too intense. He was a truly inspirational leader. Every time he spoke he would say the right thing. It can drive us on but it is an emotional day for everyone."
Ireland, who had avoided any serious injuries until centre Jared Payne was sent home with a fractured foot on Saturday, also lost flanker Peter O'Mahony on Monday with a damaged knee ligament sustained in the France game. Flyhalf Johnny Sexton is nursing a groin injury that could yet end his tournament.
While Ireland's strength in depth came to the fore in the second half on Sunday and Iain Henderson represents a tailor-made replacement for O'Connell, the departure of Ireland's inspirational captain was described as a "monumental loss" by fullback Rob Kearney.
"It is difficult and I felt awful for him. But it was great to see the sheer delight after the game in terms of what we had achieved, as opposed to feeling sorry for himself," Kearney said of the 108-capped O'Connell, who will continue to play club rugby with French side Toulon.
"He was just delighted and beaming from ear to ear. When you consider that he was so happy and ecstatic after the game and the pain he had been in at halftime, it's those little moments that make changing rooms after games so very special."
"That was brilliant to see and a great sign of the man that he was able to put his own woes behind him and was able to think of the team first."
(Additional reporting by Padraic Halpin; Editing by David Goodman)
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