The large stone came crashing down from 20 metres above the tourist and landed on his head, according to local sources.
Medical teams reportedly rushed to the site but were unable to revive the man, who was visiting the iconic church with his wife.
The piece of stone, a “peduccio”, fell off the right-hand transept of the basilica, local authorities said.
They added that there were no other known “critical elements” in the church, which was subject to periodic checks.
The Basilica di Santa Croce (Basilica of the Holy Cross) is one of the Tuscan capital’s most renowned churches.
The building is the principal Franciscan church in Florence, and a minor basilica of the Roman Catholic Church.
It is situated in Piazza di Santa Croce, about 800 metres south-east of the famous Duomo.
The site is the burial place of some of the most illustrious Italians, such as Michelangelo, Galileo, Machiavelli, the poet Foscolo, the philosopher Gentile and the composer Rossini.
For this reason, it is also commonly referred to as the “Temple of the Italian Glories”.