An x-ray revealed a pellet was lodged in the swan's skull.
RSPCA officers are appealing for information after a cygnet was found shot in the head at close range in South Lynn.
Due to the severity of the injury, the bird had to be put to sleep.
The charity received a report from a member of the public who saw the young mute swan staggering and collapsing when it tried to  stand in an area near the River Nar on March 1.
The cygnet was taken to the charity’s East Winch Wildlife Centre and an x-ray showed it had been shot and the pellet was still lodged in its skull.
RSPCA inspector Jon Knight, who collected the bird, said: “It’s so sad to think that this poor cygnet had to suffer as a result of someone taking pot shots.
“We want to highlight this awful incident so that people can keep an eye out for wildlife in the area, although we hope that this was an isolated incident.
“I would also like to thank the member of the public who helped this swan and kept a watchful eye until we collected the bird. I’m just sad this is not the outcome any of us wanted.”
Wildlife centre manager Alison Charles said staff suspected the pellet had been fired at close range and, as the wound was quite fresh, it had probably happened over that weekend.
“It is just so upsetting to think that someone has deliberately targeted an innocent wild animal,” she said.
Mr Knight said this had been the third swan which had been shot and taken to the centre in the last two weeks.
The other birds were rescued in Lincolnshire.