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.

Holyrood backed a series of opposition amendments following a Scottish government debate on patient safety.
They included a Lib Dem mention of a "recruitment crisis" and Labour warnings that services are "near breaking point".
This left the SNP voting against Shona Robison's amended motion, but they were defeated by opposition members.
Health Secretary Ms Robison had put forward a motion highlighting the work of the government's "world-leading" patient safety programme.
It said the programme "represents the international benchmark for safe care" and noted "the huge challenges that face the NHS in meeting the demands of an ageing population and those of integrating health and social care services".
Members unanimously backed a Conservative amendment from Donald Cameron adding that the health service is "facing severe workforce and staffing issues", and that "further action on staffing must be a priority".
Another amendment from Labour's Anas Sarwar was then passed by 62 votes to 61, adding in claims that "services are facing a situation in which demand is often outstripping supply". It also cited a report from the British Medical Association that the NHS is "near breaking point".
A further amendment from Lib Dem Alex Cole-Hamilton highlighted a "recruitment crisis" in the NHS, raising fears it could "pose a risk to patient safety", and was passed by the same margin.
The amended motion was then passed by 62 votes to 61, with SNP members voting against.

Russell Crow was rescued from the road by Helen Motteram and now lives in her home as one of the family.
When the Gladiator star saw their story online, he took to Twitter to say how "cool" it was and offer "some new songs" for the bird.
He tweeted: "Haha cool, what a nice lady Helen is to look after the poor blighter."
With crooked feet and unable to fly, the bird was at first mistaken for a crow and named in honour of the actor.
Since then, the cheeky rook has taken over Helen's home - sleeping in her bedroom, stealing her phone chargers and hiding her jewellery.
But his antics, and jealousy of Helen's husband, have also made him a minor celebrity - with his fame now reaching the Hollywood star himself.
Helen said she was "amazed" when she found out Russell Crowe was a fan.
"I tweeted Russell about a month ago saying Russell [the rook] would love to hear from him - but I didn't hear back," she said.
"I love his films and we named Russell after him so I've going to tweet him back to say he would love to meet him in person or get an autograph."
The bird, she said, can "print with his feet" and "hold a pen" so if the actor would like an autograph in exchange, it could be arranged.

It happened on the Letterkenny to Ballybofey Road, near Convoy, at 07:00 BST on Friday.
The car she was driving collided with a lorry. The driver of that vehicle was uninjured.
The road is currently closed and diversions are in place.
The RSPCA is trying to find a man who was caught on CCTV kicking a cat "very hard" into the air.
[NEXT_CONCEPT]
MSPs have passed a motion warning that patient safety is at risk amid a "recruitment crisis" in the NHS.
[NEXT_CONCEPT]
Oscar-winning actor Russell Crowe has tweeted support for his namesake - a disabled rook from Gloucestershire.
[NEXT_CONCEPT]
A woman in her 20s has died in a collision between a car and a lorry in County Donegal.