Winger Aiden McGeady, defender Sean St Ledger and back-up midfielder Joey O'Brien have all pulled out of Giovanni Trapattoni's squad through injury.
All three players have had knee injuries, and it was determined they would be unavailable for the games next Friday, September 6, in Dublin and the following Tuesday, September 10, in Vienna.
The Football Association of Ireland announced: "Aiden McGeady pulled out of training with Spartak Moscow this week with an ongoing knee injury, while Sean St Ledger is still working his way back to full fitness after injuring his knee in early August. West Ham's Joey O'Brien is also suffering from a knee injury and is undergoing treatment at his club."
St Ledger began the season positively for Leicester, scoring the winning goal in a League Cup tie against Wycombe, but has not played for three weeks.
O'Brien played for West Ham at Newcastle last weekend, while McGeady has not been involved for Spartak since August 4.
The FAI said Trapattoni, who also lost Derby midfielder Jeff Hendrick from his squad on Wednesday, had no plans to call in any replacements.
The results of the two games are likely to go a long way towards determining which of the Republic, Sweden and Austria finishes second in the group behind current leaders Germany.