Video posted on social media shows demonstrators cheering as dozens of beams of light focus on one of the surveillance devices in the captial Santiago.
The police drone is seen to veer out of control before dropping from the sky, possibly as a result of interference with its sensors, on 12 November.
It came three days after Chilean police warned that using lasers against their helicopter pilots was a crime because it “poses a risk to the safety of the flight and the health of the crew”.
The tactic appears to have spread from Hong Kong, where protesters used lasers to blind security forces and avoid facial recognition cameras.
Another video from Santiago, posted on Facebook on Tuesday under the title “Laser Battle”, shows protesters aiming lasers at shotgun-wielding riot police as an armoured vehicle retreats in flames.
The demonstrations in Chile began a month ago as a protest over subway fares before quickly expanding into a mass movement against inequality. At least 25 people have died and thousands have been injured.
On Friday the main political parties responded to the unrest by calling for a new constitution to replace the one imposed in 1980 by the military dictatorship under Augusto Pinochet.
— PIENSA.PRENSA (@PiensaPrensa)November 13, 2019
Under their agreement, the public will vote in a referendum on April 2020 on how to draft that new document.
“They are hearing what the people have been asking for so long,” said Pedro Alastuey, a 36-year-old physical education teacher who took part in some of the protests.
However he said it was unlikely to bring a halt to the movement, adding: “Until they give a concrete solution to the demands of the people, it will be very hard to stop this.”
The Pinochet government, which overthrew the democratically-elected president Salvador Allende in 1973, killed or tortured thousands of suspected leftists.
While Chile is one of South America’s most prosperous countries, it is plagued by high levels of poverty. More than 1.2 million pensioners receive far less than the minimum wage and many middle-class Chileans find themselves trapped by student debt.
Additional reporting by Associated Press