DoC biodiversity ranger David Moss said they were investigating.
"Shooting the falcon was unacceptable, no matter what the circumstances.
"It was a direct hit from a low calibre weapon, such as a .22 and appears to be intentional," he said.
"For someone to shoot this bird is appalling.
"Not only is the karearea a threatened species, it is a symbol of New Zealand and graces our $20 note."
He said the young bird was probably the offspring of a pair nested nearby.
The New Zealand falcon, which can reach speeds of up to 100km/h, is recognised for hunting a range of large prey such as mammals and lizards, with other birds making up most of its diet.
"Birds are their natural food source and unfortunately, this can include domestic poultry, doves and pigeons," Mr Moss said.
"If people experience problems with falcons attacking domestic birds, contact your local DoC office for advice, but don't shoot them."
¦DoC is appealing for information about the shooting and asks people to contact the Kapiti Wellington office on 04 470 8412.