A fragment of masonry fell from on the church's walls and hit a visitor, identified as 52-year-old Daniel Testor Schnell of Barcelona, on Thursday afternoon.
Schnell, who was visiting Florence with his wife, is said to have died at the scene.
Other visitors were swiftly escorted out of the church and it has been closed to the public ever since. It will remain off-limits until authorities are sure it is safe.
The 15th-century basilica, considered one of Italy's most beautiful, is checked regularly for wear. The Opera di Santa Croce, the organization in charge of running the church, says the latest survey was carried out just a week ago.
Inside the Basilica di Santa Croce. Photo: Rodrigo Soldon/Flickr
Florence's authorities have opened an investigation into the accident, which consumer rights watchdog Codacons described as “an unacceptable incident”.
It urged the Italian government to increase safety checks in all of the country's monuments.
In July, a piece of plaster came loose from the ceiling of Sicily's Acireale Cathedral, seriously wounding one man and a child. In October 2012, a cornice fell from the wall of the Caserta Palace near Naples, without causing any injuries.
In Santa Croce, the lethal fragment fell from just below the ceiling of the basilica, some 20 metres up, according to Ansa news agency. It is thought to have come loose from a “peduccio”, a piece of decorative stonework designed to support the beams that criss-cross the church's ceiling.
One of Florence's most visited churches, Santa Croce is the last resting place of famous Italians including Michelangelo, Galileo and Machiavelli.