Defence Minister Irakli Alasania told Georgian TV the servicemen had been killed when a suicide bomber drove a lorry carrying explosives into their base in Helmand province.
In all, 22 Georgian troops have been killed in Afghanistan since 2009.
Although not a member of Nato, Georgia has taken part in several missions.
With 1,570 soldiers serving in Helmand province, it has the biggest non-Nato contingent in Afghanistan.
In his televised statement, Mr Alasania said the militants who had broken into the base had all been killed.
Giving his condolences to the families of the three dead soldiers, he said other members of their battalion, the 42nd, had also been wounded.
Before Monday’s attack, the deadliest incident involving Georgian forces in Afghanistan occurred three years ago, when a landmine explosion killed four soldiers, including a colonel.
The former Soviet republic has also sent forces to Kosovo and Iraq.