Everton midfielder has started the Premier League season in terrific form but will not be making the trip to Astana
Gibson has not reported an injury but claims he is not yet ready to return to the international arena following a disappointing Euro 2012.
The former Manchester United midfielder played no part in Poland but is viewed as a key member for the upcoming campaign to qualify for World Cup 2014 in Brazil.
The 24-year-old has played a significant part in Everton's strong start to the English Premier League season and his decision to withdraw is a major blow to Giovanni Trapattoni's side.
Trapattoni said: "When Darron informed me of his decision to withdraw, I called him to talk things through. As we embark upon a brand new campaign, he is very much in my plans and I consider him to be a key player for Ireland for this campaign.
"However, Darron has said that although he doesn’t want to let anyone down, he doesn’t feel ready to ready to return to the squad for this fixture after the disappointment of Euro 2012. I hope that Darron will take this time to reflect positively on his international career, and return to us in time for the Germany game in October."
Sunderland midfielder David Meyler has been called up to the squad and will join up with the rest Dublin on Sunday afternoon.