Kazakhstan was earlier scheduled to take part in the Cooperative Longbow/Cooperative Lancer-2009 command-and-staff exercise, which Russia has criticized as unhelpful in the wake of last summer's armed conflict between Russia and Georgia over South Ossetia.
Explaining Kazakhstan's decision, Danial Akhmetov said: "We are too busy for this".
The exercise will be held from May 6 through June 1 in Georgia, and will involve 1,300 troops from 19 NATO member or ally states, but will not feature light or heavy weaponry.
The drills are aimed at improving interoperability between NATO and partner countries, within the framework of Partnership for Peace, Mediterranean Dialogue and Istanbul Cooperation Initiative programs.
Russian President Dmitry Medvedev warned last Friday that Russia "will be closely watching" the drills and will "if necessary, make appropriate decisions."
Russia's NATO envoy Dmitry Rogozin claimed on Tuesday that the planned exercises were an attempt at interference in Georgia's internal affairs.
Rogozin said the drills were a show of support for beleaguered Georgian President Mikheil Saakashvili, and would only increase tensions in the region.
NATO has said the drills are open to all ally states, and that Russia would be welcome to join.