The assaults occurred on Belloza Manner in Mernda round 4.50pm on Wednesday, February 16, leaving one cat severely injured.
The primary assault was caught on CCTV, with footage launched by police displaying the person chasing after and kicking a black and white cat.
The person allegedly then picked up a chunk of wooden and hit one other cat with it, in response to police.
The 15-year-old ginger cat was severely injured and has been left with an ongoing leg harm.
Police have launched CCTV footage and pictures of the person as they attempt to observe him down.
He's perceived to be Caucasian in look, roughly 185cm tall, with a slim construct and darkish hair.
He was sporting blue footwear, blue mid-length socks, black shorts, a black t-shirt, black watch, black sun shades and a gray cap.
Anybody who recognises the person or with data is urged to contact Crime Stoppers on 1800 333 000 or make a report on-line at www.crimestoppersvic.com.au.