Coach Steve Hansen confirmed fullback Ben Smith and flanker Sam Cane were injured in the 21-9 win in Dublin and would miss Saturday's match at Stade de France.
Smith suffered a compound fracture in his finger while Cane sprained his ankle.
Lock Patrick Tuipulotu had also left the squad to fly home for "personal reasons", the team said, while Hansen could also lose centre Malakai Fekitoa to suspension after he and Cane were cited for dangerous tackles.
Hansen said the All Blacks would contest the charge against Cane, believing he had clashed heads with Robbie Henshaw rather than committed an illegal tackle.
However, they will not defend Fekitoa for his "clumsy and high" tackle on Simon Zebo which drew a yellow card from referee Jaco Peyper.
The players' hearings are scheduled for later on Monday in London and Hansen hopes to attend both while in town for a coaches conference.
Regardless of the outcomes, Hansen will be forced to re-jig his side for Les Bleus, who were pipped 25-23 at home by Australia at the weekend.
The coach said he would rely on the existing squad to fill the holes and not fly in reinforcements.
That means Ardie Savea or Matt Todd will replace Cane at openside flanker, with Israel Dagg or flyhalf Beauden Barrett both capable of starting at fullback.
The All Blacks avenged their shock loss to Ireland in Chicago two weeks ago, which snapped their record run of 18 successive wins and gave the Irish their first ever win over New Zealand in 111 years.
Persistent questioning from Irish media over the All Blacks' tackling took some of the gloss off Saturday's win for Hansen, and hooker Dane Coles defended the team's physical game upon arriving in Paris.
"We can't control what other people say, all we can control is our performance and the way we play rugby and if people don't like that then obviously you can't please everyone," Coles said.
"We take a lot of pride in playing the game in the right way and in our performance."
(Reporting by Ian Ransom in Melbourne; Editing by Peter Rutherford)
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