The attacks took place on Belloza Way in Mernda at around 4.50pm on Wednesday February 16, leaving a seriously injured cat.
The first attack was caught on CCTV, with footage released by police showing the man chasing and kicking a black and white cat.
The man then picked up a piece of wood and hit another cat with it, police said.
The 15-year-old ginger cat was seriously injured and is suffering from a leg injury.
Police have released CCTV footage and footage of the man as they try to find him.
He is perceived to be Caucasian in appearance, around 185cm tall, with a slim build and dark hair.
He wore blue shoes, blue knee high socks, black shorts, a black t-shirt, a black watch, black sunglasses and a gray cap.