Martin O'Neill's men travel to Tbilisi on the back of a home friendly win over Oman.
Goals from Kevin Doyle and Alex Pearce secured a comfortable 2-0 victory for Ireland on Wednesday, but Wigan winger McClean did not make the bench for that game and has subsequently been withdrawn from the squad due to fitness concerns.
McClean has been a key player for O'Neill, who took over the reins of the national team last November following the departure of Giovanni Trapattoni.
And the absence of the 25-year-old represents a significant blow ahead of O'Neill's first competitive game in charge.
The Ireland boss said: "My concern really is while the injury has healed up he hasn't played that much contact football.
"It's not that he's picked up a fresh injury or anything like that."
After a disappointing appearance at Euro 2012 and their failure to reach the 2014 World Cup, Ireland will be eager to make a flying start to this latest campaign against a Georgia side managed by former Newcastle United and Wolves midfielder Temuri Ketsbaia.
A tricky-looking Group D also includes Germany, Poland, Scotland and Gibraltar, but - with the European Championship expanding to 24 teams for its latest edition - Ireland have high hopes of securing qualification.
Shay Given was handed a first start in more than two years against Oman as O'Neill rested a host of senior players, but it remains to be seen whether the veteran goalkeeper will keep his place.
While Ireland will start Sunday's game as favourites, Everton midfielder James McCarthy is not underestimating the threat posed by Georgia, who produced encouraging displays against France and Spain during their last set of World Cup qualifiers.
Speaking to the Irish Mirror, McCarthy said: "France drew 0-0 over there and Spain just about beat them [1-0] so we know it's not going to be easy."
Georgia have generally proved well organised under Ketsbaia, who has been in charge of the team since 2009.
However, goals have proved tough to come by, evidenced by a return of three goals in eight matches during their World Cup qualifying campaign.
Ireland and Georgia last met as recently as June 2013, with the former running out 4-0 winners in a friendly on home soil. However, Georgia were hampered by the 20th-minute dismissal of goalkeeper Giorgi Loria.
