Three fires were started at the site and an investigation into suspected arson is under way, Prosecutor Pierre Sennes said.
The blaze destroyed stained glass windows and the grand organ at the Saint-Pierre-et-Saint-Paul cathedral, which dates from the 15th Century.
It comes a year after the devastating fire at Notre-Dame cathedral in Paris.
But the local fire chief said the fire in Nantes had been contained and was "not a Notre-Dame scenario".
"The damage is concentrated on the organ, which appears to be completely destroyed. The platform it is situated on is very unstable and risks collapsing," Laurent Ferlay told reporters.
The cathedral roof had not been touched by the blaze, he said.
President Emmanuel Macron has reacted, tweeting: "After Notre-Dame, the St Peter and St. Paul Cathedral is in flames. Support to the firefighters who are taking all the risks to save the Gothic jewel."
The French fire service tweeted footage of the blaze.