"We view this consistent 'development' of Georgian territory by NATO soldiers as a provocative move, aiming to deliberately destabilise the military-political situation in the Caucasus region," it said in a statement.
Moscow and Tbilisi fought a brief war in 2008 due to a dispute regarding South Ossetia, a separatist region of Georgia which is funded and backed by Russia.
After the war, Russia recognised South Ossetia and Abkhazia, another breakaway Georgian territory, as independent states and stationed permanent military bases there.
The Russian foreign ministry accused Washington of "indulging Tbilisi's revanchist drive."
Moscow has accused NATO of seeking to counter it militarily in Eastern Europe with increased forces and drills, but the alliance argues it is responding to Russia's annexation of Crimea from Ukraine.
The exercise in Georgia, called Noble Partner, will involve about 1,300 participants from US, Britain and Georgia and take place at the Vaziani base outside Tbilisi for two weeks this month, starting on May 11.
Georgia, an ex-Soviet mountainous country, has bid to join the alliance, infuriating its former imperial master Russia, which bitterly opposes NATO's expansion into former Soviet republics.
The country is not however on a formal path to eventual membership.
