Georgian media reported the three Russian servicemen were detained in the Zugdidi area, in western Georgia, today.
They are accused of illegally crossing the border, a crime which carries a maximum sentence of five years in prison.
Georgian officials said the military truck had gone to Rostov-on-Don, in Russia, and had illegally brought back cargo for military units in Georgia.
The three officers are being held at a police detention facility in the town of Poti.
The military truck has also been taken to Poti. A criminal case has already been opened.