Mirko Curti said he and a friend were following the cat when it scampered towards a low rock cliff near his home in a residential area of the city.
"The cat managed to get into a grotto and we followed the sound of its meowing," he said.
In an opening in the cliff the two men found niches dug into the rock similar to those used by the Romans to hold funeral urns, and also saw human bones scattered on the floor, the British newspaper The Guardian reported Thursday.
Archaeologists who examined the site said the tomb probably dated from the 1st century B.C. and the 2nd century A.D.
Heavy rains earlier in the week probably caused rocks concealing the entrance to the tomb to crumble, they said.