Putin traveled last weekend to a resort town in the breakaway republic. His visit coincided with the 5th anniversary of Russia's recognition of Abkhazia as an independent country.
Russia and Georgia went to war briefly over Abkhazia and breakaway counterpart South Ossetia.
Georgian Prime Minister Bidzina Ivanishvili tilted toward Moscow when he brought his government to power in October. The government, however, issued a formal protest against Putin's visit to the Black Sea resort city.
"We condemn this [visit], as this is another infringement on Georgia's territorial integrity and sovereignty," Russia's state news agency RIA Novosti quoted Georgian Foreign Minister Maia Pandzhikidze as saying Monday.
Pandzhikidze said during an Aug. 8 ceremony marking the war anniversary there was little chance for a thaw in the relationship with Russia.
Georgia has lobbied for a closer relationship with NATO and the European Union. The EU has expressed frustration with the pace of political reforms in Tbilisi, saying the October election was not up to European standards.