Mirko Curti and a friend were following the cat when it scampered towards a low tufa rock cliff close to his home near Via di Pietralata in a residential area of the city.
"The cat managed to get into a grotto and we followed the sound of its miaowing," the Guardian quoted Curti as saying.
Catacombs are human-made subterranean passageways for religious practice or used as a burial place.
Inside the small opening in the cliff, Curti and his friend found themselves surrounded by niches dug into the rock similar to those used by the Romans to hold funeral urns, while what appeared to be human bones littered the floor.
Archaeologists called to the scene said the tomb probably dated from between the 1st century BC and the 2nd century AD.
Since the niches were used to store ashes in urns, the bones had probably tumbled into the tomb from a separate burial space higher up inside the cliff.
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They added that heavy rains at the start of the week had probably caused rocks concealing the entrance to the tomb to crumble, the report said.
Curti said he was nonetheless amazed to wander into a tomb so close to his house, calling it "the most incredible experience" of his life.