The Taliban claimed responsibility for the Thursday attack in a text message sent to journalists, The New York Times reported.
It was the second terror attack on a Georgian base in Helmand province in less than a month. On May 13, a suicide blast killed three people and injured several others.
Thirty Georgian soldiers have been killed in Afghanistan, the Times said.
The Georgian contingent of 1,570 soldiers is based in one of the most dangerous areas of the country.
Georgia, the largest non-NATO contributor to the International Security Force, said last year its troops will remain in Afghanistan after NATO withdraws in 2014.