The former Chelsea man can be seen in the disturbing video kicking, dropping and slapping the cat while his friends laugh.
Zouma then chases the cat and throws shoes at it before slapping its head.
West Ham defender Kurt Zouma has apologised after a video emerged of him abusing his pet cat.
"I want to apologise for my actions," Zouma told The Sun. "There are no excuses for my behaviour, which I sincerely regret.
"I also want to say how deeply sorry I am to anyone who was upset by the video. I would like to assure everyone that our two cats are perfectly fine and healthy.
"They are loved and cherished by our entire family, and this behaviour was an isolated incident that will not happen again."
There is growing pressure on the RSPCA to act following the release of the video, which has been viewed more than five million times on different accounts on social media.
The RSPCA has condemned the "very upsetting" video and reaffirmed a commitment to investigate any complaints about animal welfare.
"This is a very upsetting video. It's never acceptable to kick, hit or slap an animal, for punishment or otherwise," a spokesperson for animal welfare charity the RSPCA said.
"We are so grateful to people who report suspected animal suffering to us and we would like to reassure people we will always look into and, if necessary, investigate any complaints made to us about animal welfare."
Consequences await for Zouma at West Ham
West Ham were also quick to issue a statement and vowed there would be consequences for the Frenchman.
"West Ham United unreservedly condemns the actions of our player, Kurt Zouma, in the video that has circulated," the West Ham statement to The Sun read.
"We have spoken to Kurt and will be dealing with the matter internally, but we would like to make it clear that we in no way condone cruelty towards animals."
Professional Footballers' Association chief executive Maheta Molango also spoke about the matter at a parliamentary select committee hearing on Tuesday.
"It is not for us to discipline him - it is for the employer to discipline - but our role is to tell the player this type of behaviour is not acceptable.
"I haven't seen the video but I read he has apologised, which is hopefully a sign from him that this type of behaviour is not acceptable."
Dr Maggie Roberts, Director of Veterinary Services at Cats Protection, also issued a statement which read: "Causing any animal unnecessary suffering is a criminal offence under the Animal Welfare Act 2006. Any person seen or suspected of treating an animal badly, whether this is physical violence, neglect or any other form of cruelty should be reported to the RSPCA.
"The police work closely with the RSPCA to investigate cases of animal cruelty.
"Kicking, hitting and slapping cats or any other animal is not only illegal but will cause serious bodily harm. This cat may have been subjected to broken bones or other injuries through being mistreated in this way.
"We noticed that some people viewing the video online thought it was funny. We can assure them that this is not a laughing matter."
Zouma starts vs Watford
Despite the ongoing investigation into the video, Zouma was named in West Ham's starting lineup vs Watford on Tuesday night.
It came as a surprise to many, with BT Sport pundit and former West Ham player Joe Root labelling it a "miscalculation by the club".
"From West Ham's perspective, I can see why they probably want to let it settle, get the game out of the way, and deal with it internally. But I think it's a miscalculation by the club - he could have sat this one out.
"But he's here, he's starting. It's an unusual disciplinary matter, I don't remember seeing animal cruelty within football. I'm surprised he's in tonight."
Fellow pundit Owen Hargreaves added: "I'm really surprised. He's their best centre-back but I thought he'd be out for at least a couple of games. This won't be the end of this, it puts a lot of pressure on him and the football club."
David Moyes was also questioned whether the video affected his decision to start the Frenchman, to which he responded "No, because he's one of our better players.
"But it's certainly ongoing and the club are dealing with it, so that's a separate matter."
Yoan Zouma 'taking time to reflect' on actions
A statement below was released by Dagenham & Redbridge and Yoan Zouma.
Dagenham & Redbridge FC condemns the actions of our player Yoan Zouma in filming the video that has circulated of his brother, and his reactions to the events shown.
Since first becoming aware of the incident this morning the club has had discussions with Yoan and we will now take some time to consider our response, which we will of course make public in due course.
However, in the meantime we would like to make it completely clear that we in no way condone any form of cruelty towards animals and take this matter very seriously.
"I deeply regret my involvement in the video that has been widely circulated and unreservedly apologise, not only for my actions, but for the upset and distress this will have caused to so many people," said Yoan Zouma.
"I am now taking time to reflect on what I have done but wish to assure everyone that this was an isolated incident and not something that I am proud of."