The landslide happened in the early hours of the morning in the village of Nergeti, some 170 kilometres from the Black Sea nation's capital Tbilisi.
"Rescuers found four bodies and a search operation is underway to find five missing people," the head of Georgia's emergency situations service, Temur Mgebrishvili, told journalists.
President Salome Zurabishvili expressed "deep sorrow over the tragic loss of life in the natural calamity".
"I offer my condolences to the families of victims and hope that those missing will soon be found," she said.
Heavy rains and flooding are fairly common in Georgia, where steep slopes pose a regular risk of landslides.
In August last year, a landslide at a resort town in northwestern Georgia killed 26 people.
In 2008, six people died in a landslide in the southern Black Sea region of Adjara.
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