The local priest urged residents to try to save the church. They rushed to a nearby river to collect water, but it was too late.
The building is still standing but most of the church’s ornate interior has been destroyed, including work by indigenous artist Diego Quispe Tito.
Peruvian fashion photographer Mario Testino, who is also president of the World Monuments Fund Peru, told the BBC it was a “tragic loss” for the country. He said the cultural ministry had pledged to restore the church.
“The entire roof has been consumed by the fire,” said fire chief, Jesus Valdivia.
“Saint sculptures, images, paintings from the Cuzco culture have virtually disappeared, 80 percent of it inside the church.”
Cuzco Mayor Carlos Moscoso broke into tears when he saw the extent of the damage.
The church had undergone extensive restoration work between 2008 and 2013.
A local journalist, Javier Farje, said “it’s devastating. This church represents the merge of two cultures – European art, mainly the Flemish school of painting, and the Andean school of art.”
The city of Cuzco was the capital of the Inca Empire, which was destroyed by the Spanish conquest of most of the Americas.