Police sources said the officers shot at the man when he kept threatening them with the hammer.
French interior minister Gerard Colomb told reporters that the attacker, believed to be an Algerian student, was also armed with kitchen knives.
"We've gone from very sophisticated terrorism, now we are at a point where we have this basic terrorism using any basic tools they can find," Colomb said.
One officer was lightly injured and the assailant was shot in the chest, according to one source.
Emergency responders were on scene after the attack, according to Europe 1 radio network.
A man who attacked a police officer laying wounded on the esplanade of Notre Dame cathedral in Paris. Photo / AP
Police had earlier said they were dealing with an incident in the courtyard outside the world-famous tourist site amid reports of panic and gunshots in the area.
Officials warned people to stay away from the area.
At least one person said on Twitter that he was inside the church and could hear sirens outside.
"So we are trapped in Notre Dame Cathedral," Matthew CurrieHolmes wrote on Twitter. "Something is happening outside we don't know what it is. Police sirens can be heard."
He later said that officials were not letting anyone in or out of the cathedral.
A month earlier a convicted criminal with links to radical Islam shouted "I am here to die for Allah, there will be deaths" seconds before he was shot dead during an attack at Paris Orly airport.
The 39-year-old, named locally as career criminal Ziyed Ben Belgacem, was killed after wrestling a soldier's gun from her and fleeing into a McDonald's. He sent a text message to his brother and father stating "I shot the police", shortly before he was killed.
It followed the shooting in February of a man outside the Louvre museum in the heart of Paris after he attempted to storm the historic art gallery.
On July 14 last year amid Bastille Day celebrations in the Riviera city of Nice, a large truck was driven into a festive crowd, killing 86 people. The driver was shot dead. Isis extremists claimed responsibility for the attack.
Police officers seal off the access to Notre Dame cathedral in Paris, France. Photo / AP
Just 12 days later two Isis fanatics stormed into a church in Normandy and slit the throat of a priest as he was celebrating mass.
A month earlier, two French police officers were murdered in their Paris home in front of their 3-year-old son. Again Isis claimed responsibility for the slaying, which was done by a jihadist with a prior terrorist conviction. He was killed by police on the scene.
And in November 2015, Isis militants went on the rampage, murdering 130 people.
They used machine guns to slaughter revellers at the Bataclan music hall and in bars and restaurants in some of the city's most popular night spots. A suicide bomber also targeted the Stade de France stadium.
The atrocity led to the declaration of a state of emergency in France.
In January the same year, two brothers killed 11 people inside the Paris building where the satirical magazine Charlie Hebdo was headquartered in what Isis claimed was retaliation for the publication of cartoons about the Prophet Muhammad.
More were killed in attacks on a kosher market in eastern Paris and on police. There were 17 victims in all, including two police officers. The attackers were killed.
