
The carcass of the male bird was found by a member of the public outside the East Mill in Belper.
It was taken to a vet and an x-ray showed that a shot was lodged in its shoulder.
Peregrine falcons are fully protected by legislation, which makes it an offence to deliberately kill or injure them.
Derbyshire police’s specialist wildlife officers are investigating the offence in partnership with the trust and the RSPB.
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The RSPB is also offering a £1,000 reward for information leading to the conviction of the person responsible.
Tim Birch, from the trust, said: “We have all been shocked by the shooting of the male peregrine at our headquarters in Belper.
“To have a wildlife crime happening right on our doorstep is both alarming and upsetting.
“Many people from Belper, and indeed from around the whole region, have been thrilled to watch peregrines around the mill where we work.
“We feel very privileged to have these birds living alongside us.
“We strongly condemn the shooting of this bird.”
Sergeant Darren Belfield, from Derbyshire police, said: “Birds of prey, such as the peregrine falcon, are fully protected by legislation.
“The perpetrators of this cruel and deliberate act have shown a clear disregard for the law surrounding this species.”
The bird was found dead on January 17.
Anyone with information should call Derbyshire police on 101 or Crimestoppers on 0800 555 111.