A swan and two of her cygnets were killed in an attack with what was believed to have been a catapult.
The deaths on the River Thames at Cricklade, Wiltshire, were condemned by member of a local Facebook group who described the attackers as "evil".
Wiltshire Police received reports of the deaths on Friday and said inquiries were continuing.
Some local people have started patrolling the area to try to protect surviving birds.
The incident was variously described as "heartbreaking", "shameful and evil" and "sad and disgusting" by some members of the local Facebook group that initially reported it.
A Wiltshire Police spokesperson said: "We know there is great concern amongst the local community, so [we] want to reassure people that inquiries are being carried out and we will be conducting patrols in the area to speak to potential witnesses and prevent any further incidents."
Under the Wildlife and Countryside Act 1981, anyone prosecuted for deliberately trying to injure, kill or take a wild bird can face up to six months in prison and an unlimited fine.