The ministry said it had summoned the Russian ambassador in Tbilisi, Vyacheslav Kovalenko, to protest against the visit, which was not coordinated with Georgian authorities.
"It was reiterated that while crossing the Georgian-Russian state border, it is obligatory to implement procedures set out by Georgian law - in particular, legitimate checkpoints must be used," the ministry said.
"Such visits, and any contacts with representatives of the separatist regime are inadmissible without the agreement of Georgia's central authorities," the ministry said.
Relations between the ex-Soviet neighbors, strained over Moscow's alleged support for separatist movements in Georgian breakaway territories and trade disputes, hit a low point in September, with Tbilisi's brief detention of Russian officers on spying charges. During the feud that followed, Moscow withdrew its diplomats, suspended transport and mail links and clamped down on 'illegal' Georgian businesses.
Russia has since restored postal links with Georgia and returned its ambassador and diplomatic staff.
Kovalenko played down differences between Tblisi and Moscow.
"There are no insoluble contradictions in relations between Russia and Georgia. Russia does not question Georgia's sovereignty and independence or its territorial integrity, but obviously on the condition that the legal interests of all peoples living in the country are observed," he told a video conference in Tbilisi.
Kovalenko also said Russia will start issuing visas to Georgian nationals as soon as a certain technical issues are resolved.
Pro-Western Georgian President Mikheil Saakashvili, who swept into power on the back of a "color" revolution in 2003, has pledged to bring the breakaway regions of Abkhazia and South Ossetia back under Tbilisi's control, and accuses Russia of backing separatists in the regions, a charge that Moscow denies.
