The bodies of the three protected red kites were discovered in the Tregynon area, near Newtown, on Sunday evening.
A villager was out walking with her family when she found two of the dead birds of prey. She said her examination of the birds suggested they had been shot.
She took a photograph of the birds and had planned to return to the spot to collect the bodies on Monday, but they had disappeared overnight.
The body of a third red kite was discovered by another walker and she put it in a safe location where it was later recovered by wildlife broadcaster and author Iolo Williams and his sons on Sunday night.
He had the body x-rayed by veterinary surgeons in Montgomery who discovered that it had been killed by a shotgun.
“This is a horrific incident,” said Mr Williams, former species officer for the RSPB in Wales who helped to re-establish the red kite in Wales.
“I don’t think there has ever been a case in Wales where three red kites have been shot.
“The bodies of two of the red kites disappeared after the lady that found them posted the shocking discovery on social media. I suspect they were taken by the person who shot them to try to cover their tracks, but that person probably didn’t think we would discover the third body.
“I am mystified why anybody would want to kill these red kites. The result of their criminal action means that eggs in two or three nests will now also be destroyed.”
Anybody found guilty of killing a bird of prey without a licence could face up to six months in prison or a fine of up to £5,000 for each bird under the Wildlife and Countryside Act 1981.
Police Chief Inspector Andy Pitt confirmed that Powys Rural Crime Team were investigating a report that three red kites were found in the Tregynon area on Sunday, having been shot.
“There is absolutely no excuse for anyone to have committed this cruel act against these protected wild birds which are themselves the symbol of our county,” he said.
“I would ask anyone with information about who is responsible to contact the Powys Rural Crime Team via the 101 number.”
RSPB Cymru’s head of species Julian Hughes said: “Red kites have made a comeback in Wales after a collaborated effort by farmers, conservationists and communities. For most of us, the sight of these glorious birds – recognisable by their long wings and forked red tail – is a source of joy.
“They should be celebrated, not persecuted. If you have any information which may help with the police’s investigation, please contact the police on 101 immediately.”
The destruction of the protected birds of prey has caused outrage in the village where they were often seen soaring overhead.
Local Powys County Councillor Heulwen Hulme said: “This is extremely worrying and the second incident within this small rural community within a week.
"Earlier last week, a loose dog killed five sheep and mauled 11. Now we have three red kites killed by a shotgun and left for members of the public to see.
“Due to the power of social media, two of the birds were later removed before the RSPB and police could attend. Someone out there knows something about both incidents. These actions will not be tolerated and I ask every member of our community to be vigilant and report anything they consider suspicious to the relevant authority.”
A graceful bird of prey, the red kite is unmistakable with its reddish-brown body, angled wings and deeply forked tail.
It was saved from national extinction by one of the world's longest-running protection programmes. Red kites are fully protected and listed under Schedule 1 of The Wildlife and Countryside Act.