The pair of birds, who were believed to have been together over a decade, were discovered in a village in Hampshire.
The female died before it could receive treatment while the male is being cared for at the Sanctuary.
The charity says he is calling for his mate.
X-rays showed he had three ball bearings in his neck.
Those who are discovered to have killed a mute swan, which is a protected bird, will have to pay a fine of up to £5,000.
Swans usually mate for life, although “divorce” sometimes occurs, particularly following nesting failure, and if a mate dies, the remaining swan will take up with another.
The Swan Sanctuary is petitioning Parliament to make the sale of catapults/ammunition and carrying catapults in public illegal following a spate of recent attacks on swans.