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 fire began in the early morning, with massive flames visible from outside the building. More than 100 firefighters brought it under control after several hours.
Newsagent Jean-Yves Burban said he heard a bang at about 07:30 local time (05:30 GMT) and saw flames when he went out to see what was happening.
“I am shook up because I’ve been here eight years and I see the cathedral every morning and evening. It’s our cathedral and I’ve got tears in my eyes,” he told Reuters.