The Flybe plane was travelling at about 900 feet (274 metres) and was about 2 miles (3 kilometres) from Cornwall Airport Newquay when it reported the incident on Tuesday, police said.
Devon and Cornwall Police conducted a search of the area but have not found the drone or operator, the BBC reported.
Inspector Dave Meredith called it "an incredibly concerning incident".
"The close proximity of the drone to the passenger aircraft shows a complete disregard by the operator for public safety and we are appealing to the public for information to help us track down this reckless drone operator," Meredith said.
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"Although on this occasion there was no danger of collision, Air Traffic Control (ATC) reported this incident to the police as the drone should not have been flown in that area without ATC clearance and posed a potential danger to incoming flights," she said.
The plane involved in the drone near-miss was an ATR 72, a twin-engine turboprop which is popular on short-haul routes.
The incident was the latest in a series involving drones and commercial aircraft.
On April 17, police said a British Airways passenger jet from Geneva, with 132 passengers and five crew on board, was hit by what most likely was a drone as it prepared to land at London's Heathrow Airport, Europe's busiest airport.
The plane landed safely but the increasing use of drones for commercial purposes, photography or leisure has led to fears they pose a serious risk to passenger aircraft.
Britain's Civil Aviation Authority says there were some 40 near-misses between drones and aircraft in 2015.