Police are investigating an animal cruelty matter in Burnie, after a pet cat was found to have been shot with an arrow earlier this month.

The cat, Noah, was found with significant injuries in Downlands about 5:30pm on Sunday 2 July.

Noah subsequently underwent emergency surgery and is recovering.

Anyone with information about the incident is asked to contact Burnie Police on 131 444 and quote OR717081.

Information can be provided anonymously to Crime Stoppers at crimestopperstas.com.au