The 52 year old tourist was visiting the Basilica of Santa Croce with his wife when a piece of decorative stone fell on him from a height of 66 feet.
Irene Sanesi, the head of the organisation that manages the landmark, told the Italian news agency Ansa: "We are really astonished at what has happened, and we ask ourselves how it could happen."
The Basilica of Santa Croce is renowned as the burial place of iconic Italian figures Michelangelo, Galileo Galilei and Niccolo Machiavelli.
Italy's Culture Minister Dario Franceschini said an investigation would be conducted by prosecutors to determine the cause of the incident.
The fatal accident raises fresh concern over the safety of the country's cultural heritage, which includes many fragile and aging attractions.
Over the summer, two people were seriously injured when plaster fell from the ceiling of Sicily's Acireale Cathedral during a wedding.
Four people died in the northern city of Pavia in 1989 when a 14th-century bell tower collapsed.