On Tuesday evening a group of 15 heavily armed elite police officers searched student accommodation in the suburbs of Paris, where the suspect rented a studio, an AFP journalist said.
Collomb said the officer's condition is not serious.
The vehicle was tracked to an all-female terrorist cell, allegedly acting on the orders of Syria-based Islamic State jihadists.
It is the first attack since President Emmanuel Macron won last month's election and comes days before a parliamentary poll in which opinion surveys show Macron on course to win a landslide majority. The government plans to ask parliament to extend it from July 15, its current expiration date, until November 1.
Police said the operation was over about an hour after it started.
In this image provided by Nancy Soderberg, people inside Notre Dame cathedral sit with their hands in the air, after an attack on police in Paris, Tuesday, June 6, 2017.
At least 1,000 people were told to remain inside the cathedral.
French officials are treating the incident as a terror attack, the prosecutor's office said.
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Khalid said he went into shock after the collision happened and others on the scene had to lift the van in order to remove him. The attack is the latest in a series of terrorist incidents in the United Kingdom in the past few months.
The Cathedral of Notre Dame of Paris, in English Our Lady of Paris, is one of the most famous of the Gothic cathedrals of the Middle Ages and is enormously popular with tourists.
Collomb said that police found kitchen knives and a hammer on the suspect.
France remains in a state of emergency after a series of deadly attacks by jihadis across the country since January 2015. For Paris, the incident follows an attack on April 20 on the Champs-Elysees, which left one police officer dead.
Meantime, it was frightening for the 600 people inside Notre Dame Cathedral.
Eyewitnesses said they saw a man lying on the ground.
A woman in the area at the time said she heard two shots. She said that there had been no panic inside the cathedral.
One holidaymaker wrote on Twitter: "Not the holiday experience wanted".
Lawrence Langner, a 73-year-old American visiting the neighborhood just across the Seine River from the cathedral, told The Associated Press that he suddenly heard a commotion and two detonations like gunshots. She did not provide further details.
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