A video posted Thursday by the G1 news website shows the police car chasing the plane.
The passenger-side officer leans out the window with a high-caliber rifle, preparing to fire. But the officer driving shouts: "Don't shoot! I am going to hit the wing!"
Seconds later the car smashes into the single-engine aircraft.
The officers then hop out and surround it.
Federal police spokesman Edson Geraldo de Souza tells G1 news that the pilot and four accomplices on the ground were arrested in the incident Tuesday. Nobody was hurt.