The incident is believed to have occurred near West Worthing railway station on Sunday, June 7.
Owner Lucy, who did not wish to share her surname, said her cat Beau returned home at around 5.30am with the arrow through his stomach, which a vet believed could have been from a crossbow or a “dangerous hunting weapon”.
She said: “We let our cat out at night and we never felt there was an issue.
“We heard this commotion downstairs at around 5.30am, thumping and meowing and yowling.
“I ran downstairs, it was something we couldn’t believe we were seeing.”
Lucy said the cat was rushed to the vet immediately, where he underwent surgery.
Beau then began to “slowly decline” and was put down on Monday, June 8.
The family contacted police before 9am on the day of the incident, Lucy said. Sussex Police has confirmed it is investigating.
A spokeswoman for the force said officers attended and “have been conducting a number of enquiries, including collecting CCTV and speaking with anyone who may have witnessed anything suspicious around the time of the incident”.
Sergeant David Hedgecock said: “As our investigation into this concerning incident continues, we are appealing to the public for any information or footage which could help to identify the person responsible for firing the arrow.
“If you witnessed anything in Ripley Road, or in the roads surrounding, such as The Drive, or in Tarring Road, we ask that you make a report to police.”
Reports can be made online or by calling 101 quoting reference 312 of 07/06.
Lucy has set up a Crowdfunder for support with vet bills, which has raised more than £1,100 at the time of writing. Donations can be made at crowdfunder.co.uk/p/beau-intensive-care.
She said: “I would never normally do that.
“It’s a criminal act.
“We’re left with the loss of our little family member and we have now got a huge bill to pay.”
