Reports said the bird was found near the central market in the town Zugdidi, about 300 kilometers (190 miles) west of the capital, Tbilisi.
Witnesses said the pigeon was sitting on an electricity transmission line and then suddenly plummeted to the ground. "It must have been ill with bird flu," people who gathered around the dead bird are reported to have said.
Local veterinaries examined the pigeon, and said it had not been infected with bird flu, a television channel, Imedi, said.
"There is no reason to panic," a spokesman said.
Local people suggested that the bird had been electrocuted.
The Rustavi-2 television channel said the dead pigeon had been delivered to Tbilisi for a more detailed examination.
The concerns arose after the deadly H5N1 strain of avian flu was discovered in eastern Turkey near the Georgian border. The virus has already claimed the lives of at least two people in Turkey and the World Health Organization has confirmed 14 other human cases.
Border controls have been tightened in the country, and the authorities have urged people to be careful and to refrain from hunting migrant birds.
