Georgia accuses Russia of trying to annex the territory by supporting separatist forces and encouraging residents to take up Russian citizenship. Most people in Abkhazia and South Ossetia have Russian passports.
Kenyaikin's comments were Moscow's sharpest warning so far to Georgia in its standoff with the two breakaway regions.
He said: "We don't plan anything of a military character, but should military conflicts break out on one side or another, then the initiator of these conflicts should be assured that Russia will take all possible measures to defend the interests of its countrymen and its citizens."
Kenyaikin also alleged that Georgia was massing military forces along the administrative border that separates it from Abkhazia.
The build-up "can only mean preparations for military action ... possibly in the near future. This can't be ruled out," he said.
Kenyaikin is in charge of relations with former Soviet states, and said he has "no confidence" that Washington is working in any way to resolve the standoff.
Vladimir Putin, the Russian president, initiated closer ties with both provinces, prompting international condemnation and outrage in Tbilisi.
According to Georgy Baramidze, Georgia's deputy prime minister, Russia has "crossed the line" and committed "a dangerous and provocative act" which could "destabilise the whole region".
Another flare-up occurred on April 20 when an unmanned Georgian spy plane was shot down. Georgia blames Russia, which says that Abkhaz rebels were responsible.
Georgia's pro-Western government is trying to join Nato, but the unresolved conflicts in the two northern provinces are part of the reason that the alliance has decided to delay putting the ex-Soviet republic on the path to membership.
Georgia says Russia is artificially stirring up the conflicts to weaken its independence, but Moscow accuses the Georgians of being the aggressors.