The Spartak Moscow winger was named in manager Giovanni Trapattoni's provisional 29-man squad but was absent on Saturday when the Italian cut his list to 23 players.
The Football Association of Ireland confirmed injuries had forced McGeady, Hull defender Paul McShane and Norwich winger Anthony Pilkington to withdraw.
The Republic will face Sweden in Stockholm next Friday, before tackling Austria in Dublin four days later.
McGeady has a knee problem and was not involved for Spartak in their Russian Premier League match on Saturday, while McShane has an ankle injury and Pilkington is sidelined with a hamstring strain.
Trapattoni has culled four players from his initial squad, relegating West Ham full-back Joey O'Brien, Reading centre-back Alex Pearce and the Wolves pair of midfielder Stephen Ward and striker Kevin Doyle to standby duty.
Ipswich goalkeeper Stephen Henderson is also on standby, along with Hull midfielder David Meyler.
Millwall striker Andy Keogh, who was not originally selected by Trapattoni, receives a call-up to the squad that assembles tomorrow in Malahide.
Trapattoni said: "As a manager, I am sometimes faced with some very tough decisions, but I feel that the squad I have chosen will get us the results we need from these two qualifiers.
"I have not made these choices lightly and will continue to monitor each player's progress ahead of our next challenges in May and June."
Republic of Ireland squad for World Cup qualifying matches against Sweden(March 22) and Austria (March 26):
Forde (Millwall), Westwood (Sunderland), Randolph (Motherwell); O'Shea (Sunderland) St Ledger (Leicester), Clark (Aston Villa), Wilson (Stoke), Coleman (Everton), Kelly (Reading), O'Dea (Toronto); Whelan (Stoke), McCarthy (Wigan), Green (Leeds), Hoolahan (Norwich), Hendrick (Derby), McClean (Sunderland), Brady (Hull); Keogh (Millwall), Keane, Long (West Brom), Sammon (Derby), Walters (Stoke), Cox (Nottingham Forest).
Standby: Doyle (Wolves), Ward (Wolves), O'Brien (West Ham), Pearce (Reading), Henderson (Ipswich), Meyler (Hull).