BFM TV reported the assailant had been caught after a manhunt that involved two police helicopters and more than 200 officers.
There was a shoot-out during the arrest and some policemen were slightly injured, it added. The victim was in a critical state, the news channel added.
The man, who police said stole the officer's weapon, initially fled in a car before a crash forced him to continue on foot. Schools in the area were under police protection.
The motive for the stabbing was not immediately clear.