Millie the cat has been left with a suspected broken jaw from the attack, which the RSPCA described as "sickening".
The video shows two men walking towards Millie in Derby, then one kicks her and she flies several feet in the air.
It happened outside the Guinness Trust flats in Sidney Street at about 16:25 GMT on Thursday.
RSPCA inspector Sarah Burrows said: "It is an unprovoked attack which has sadly left Millie with a suspected broken jaw.
"Inflicting such a horrific attack on a defenceless cat is sickening and it's important we track down the people responsible."
The charity asked anyone with information to contact them.
They warned that anyone found guilty of causing unnecessary suffering to an animal could face up to six months in prison and a fine of up to Â£20,000.
The RSPCA is trying to find a man who was caught on CCTV kicking a cat "very hard" into the air.