The man, a folk singer, died from septic pneumonia in a hospital in the northern town of Verria on Wednesday, a year after being diagnosed with CJD, the health ministry said.
But a senior health official insisted the case was a "one in a million" occurrence of sporadic CJD, unrelated to mad cow disease and non-transmissible.
"The man did not have (the cattle disease) Bovine Spongiform Encephalopathy," said Panayiotis Efstathiou, spokesman of Greece's national health operations centre.
"He had sporadic CJD, one of the rarest neurological diseases which can be internally caused by a virus," he told AFP.
Over 150 people around the world have died from the human form of mad cow disease, Variant Creutzfeldt-Jakob (vCJD) since it first emerged in 1995.
It is thought that the variant of the disease passed to humans who ate meat contaminated with Bovine Spongiform Encephalopathy (BSE).
Greece has had no vCJD cases in humans, Efstathiou said.
Health ministry veterinary expert Spyros Kyriakis added that there has been one case of mad cow disease in Greece, in a cow slaughtered in 2003. The animal was destroyed along with the rest of the herd.