Police said the officer used his weapon to shoot the attacker, who was then taken to hospital.
Police union official Cedric Michel said the attacker was armed with a hammer and targeted a police officer on patrol on the esplanade in front of the cathedral.
The attacker was then "neutralised" by police, he added.
It is unclear whether the attacker was acting alone.
A large number of tourists have been kept inside, while authorities have urged people to avoid the area.
Fr Aidan Troy is from St Joseph's church in central Paris.
He told Premier he visits the Cathedral three times a week and has noticed an increase in security in recent weeks.
"To enter the area in the front of the Cathedral you have to go through police surveillance and then you have security at the door," he said.
"When inside you are in a haven of peace but when you come outside you realise we are living in very disturbed times. I have noticed this increase."