Regular flights between Georgia and Russia were cancelled when a brief war between the two nations broke in August 2008 and there were no flights to Sochi dating back to before the fighting. There have been occasional flights between Georgia's capital, Tbilisi, and Moscow since 2010.
The Sochi Games have touched a nerve in Georgia, a small nation in the Caucasus Mountains bordering Russia. Many in the country remain bitter over the 2008 war, which left two separatist territories outside of Georgia's control, including Abkhazia, a territory just south of Sochi.
The Olympic host city is 450 kilometres (280 miles) from Tbilisi and only 4 1/2kilometres (just under 3 miles) from the border with Abkhazia.
Only 15 passengers were aboard the one-hour Georgian Airlines flight, company spokeswoman Nana Khutsishvili said Tuesday.