Payne missed last weekend's win against Italy after bruising his foot before returning to training this week. He was not included in Sunday's team to face France and Ireland said further scans this week revealed a foot fracture.
Payne formed a strong midfield partnership with Robbie Henshaw during last year's Six Nations triumph and the New Zealand-born centre's strength off the ball was a key feature of Ireland's miserly defence during the championship.
"It's massive in some ways. For Robbie Henshaw, Jared has been massive for him and so helpful with everyone in the team. He's a big decision maker in our team, and some of you will have picked up his defensive record as well," Ireland scrum coach Greg Feek told a news conference.
"We feel for him and it was a bit of a moment today, it's always sad to see one of your family members in the situation he's in."
Former Ireland centre Brian O'Driscoll, whose number 13 jersey Payne took over last year, said on Twitter the injury was bad news for Ireland and that Payne had been the glue that bound the team together.
Keith Earls, who offers more pace than Payne but not the same physical presence, will start at outside centre for the second game in a row in Cardiff on Sunday.
Versatile Leinster backs Luke Fitzgerald and Ian Madigan can also provide cover in midfield, along with Ulster's out-and-out centre Darren Cave.
"He's been one of our most consistent players over the last couple of years, he's been playing some outstanding rugby and of course losing a player like that is going to be a massive blow to any squad," Ireland wing Tommy Bowe told reporters.
"We know that's the nature of the competition, we've been very fortunate compared to some teams out there, but we know we've plenty of strength in depth in the squad that can fill in those positions."
No decision on a squad replacement will be made until after Sunday's Pool D decider and will come down to what happens against France, Feek said.
(Editing by Nick Mulvenney)
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