Police were contacted at 1pm on Tuesday May 9 after the animal’s body was discovered near the River Lune close to Low Road.
The swan had suffered a neck injury which officers believe was caused by a firearm.
Sgt Dylan Hrynkow, of Lancaster Police, said: “This is a very distressing and disturbing incident in which a defenceless animal has been killed.
“The swan has been found with a major neck wound, believed to be caused by a firearm.
“I understand this type of incident can be very upsetting for people and we are carrying out an investigation in order to locate those responsible.
“If you have any information about the offence, or witnessed the attack, please contact us immediately.”
Anyone with information can contact police on 101 quoting crime reference WB1704241.
Alternatively independent charity Crimestoppers can be contacted anonymously on 0800 555 111 or online at Crimestoppers-uk.org.