The cause is not yet clear, but officials say that it could be linked to renovation work.
A major operation to tackle the blaze is under way at the 850-year-old Gothic building, but the cathedral’s spire and roof have collapsed.
Last year, the Catholic Church in France appealed for funds to save the building, which was crumbling.
Hundreds of people have gathered in the streets around the cathedral, observing the flames in silence.
French President Emmanuel Macron, who has arrived at the scene, said his thoughts were with “all Catholics and all French people.”
“Like all of my countrymen, I am sad tonight to see this part of us burn.”
Mr Macron has cancelled his planned speech to the nation following the fire, an Élysée Palace official said.
A spokesman for the cathedral said the whole structure was “burning”.
The mayor of Paris described the damage as “colossal”
“There will be nothing left,” he said. “It remains to be seen whether the vault, which protects the cathedral, will be affected or not.”
The blaze broke out on Monday afternoon and an area surrounding the building has been cleared.
A symbol of a country
Analysis by Henri Astier, BBC World Online
No other site represents France quite like Notre-Dame. Its main rival as a national symbol, the Eiffel Tower, is little more than a century old. Notre-Dame has stood tall above Paris since the 1200s.
It has given its name to one of the country’s literary masterpieces. Victor Hugo’s The Hunchback of Notre-Dame is known to the French simply as Notre Dame de Paris.
The last time the cathedral suffered major damage was during the French Revolution. It survived two world wars largely unscathed.
Watching such an embodiment of the permanence of a nation burn and its spire collapse is profoundly shocking to any French person.
The mayor of Paris, Anne Hidalgo, who is already at the scene described it as a “terrible fire” and urged people to respect the boundaries set up by fire crews in order to ensure that they remain safe.
The cathedral is visited by millions of people every year
US President Donald Trump suggested “perhaps flying water tankers” could be used to extinguish the fire.
The Notre-Dame cathedral, which is visited by millions of people every year, is undergoing renovations after cracks began to appear in the stone, sparking fears the structure could become unstable.
The Paris prosecutor’s office said it has opened an inquiry into the incident.
