Police and the RSPCA have launched an investigation after the bird was found by walkers with a bullet in its wing on May 10.
It had suffered serious injuries and was taken by staff to a nearby veterinary practice for treatment.
A West Yorkshire Police spokesperson said: "X-rays revealed that the bird had been shot and a pellet was lodged in its right wing. The bird was put down by staff at the practice, as its injuries were too severe for it to survive and wouldn’t have been able to fly any distance.
"It is believed the shooting occurred close to the entry point of the public footpath into the Harewood Estate from the A659, near to the junction with the A61 at the bottom of Harewood Bank."
Red Kites and other birds of prey are commonly seen around Harewood, between Leeds and Harrogate.
Ben Lascelles, Development Manager at Harewood Estate, said: “The Harewood Estate works hard to champion conservation of Red Kites and other native wildlife, and many thousands of people visit us each year to enjoy them. To discover one of these majestic birds has been shot is particularly disappointing and upsetting.”
Howard Jones, RSPB Investigations Officer, said: “Illegal persecution is a real and persistent threat to birds of prey like red kites. They’re a wonderful sight, and the conservation effort to return these birds to our skies has been huge.
"It is disgraceful that some are spoiling this through their thoughtless and criminal actions."
Anyone with information can call West Yorkshire Police on 101 quoting crime reference number 13180232956. Anonymous information can be passed on by calling the RSPB’s confidential Raptor Crime Hotline on 0300 999 0101.