The 27-year-old has also lost his deal with sportswear giant Adidas over the disturbing video showing him dropping, kicking and slapping his pet.
The RSPCA animal welfare organisation described the video as "very upsetting" and is leading the investigation while cooperating with police.
Around 200,000 people have signed an online petition calling for Zouma to be prosecuted as the public backlash intensifies in a country renowned for its love of animals.
West Ham issued a fresh statement on Wednesday saying Zouma was complying with the RSPCA, including delivering his two cats to the charity for assessment.
"Kurt is extremely remorseful and, like everyone at the club, fully understands the depth of feeling surrounding the incident and the need for action to be taken," the club said.
"Separate to the RSPCA's investigation and pending further sanction once the outcome of that process is determined, West Ham United can confirm that Kurt Zouma has been fined the maximum amount possible following his actions in the video that circulated.
"The player has immediately accepted the fine and has requested that it is donated to animal welfare charities."
Reports said the fine would total around £250,000 ($340,000), with standard Premier League contracts allowing for a maximum fine of two weeks' wages.
The RSPCA, which is working with police on the case, tweeted that the cats were "safe and in our care".
"Our priority is and has always been the wellbeing of these cats," said a spokesman. "They've been taken for a check-up at a vets and then will remain in our care while the investigation continues.
"We're grateful to everyone who expressed their concern for these cats. We were dealing with this issue before the video went viral online and are leading the investigation."
Adidas, the defender's official personal kit supplier, confirmed it had cut ties with Zouma, saying in a statement: "We have concluded our investigation and can confirm Kurt Zouma is no longer an Adidas-contracted athlete."
Insurance and investment company Vitality announced it was suspending its sponsorship as West Ham's "official wellness partner", saying it was "distressed" by the video.
A spokesman for Heineken UK, West Ham's "beer and cider partner", said it was appalled at the contents of the video and welcomed the actions the club were taking.
West Ham had previously said they would be dealing with the matter internally, adding: "We would like to make it clear that we in no way condone cruelty towards animals."
But Zouma, who had previously apologised for his actions, was nevertheless selected by manager David Moyes for Tuesday's 1-0 win against Watford at the London Stadium.
Responding to criticism, Moyes insisted he was an "animal lover" but was adamant he had to do what was right for his club, who are fourth in the Premier League table.
Zouma got a taste of the depth of feeling as he was relentlessly booed by Watford supporters, with even West Ham fans joining in some of the jeering.
French Football Federation (FFF) president Noel Le Graet said Wednesday it was "obviously a shocking act of mistreatment."
"This gratuitous, stupid and nasty act of violence appears all the more astonishing since I have never heard anyone speaking badly of Kurt Zouma. On the contrary, he is a boy known to be respectful," Le Graet told AFP.
Maggie Roberts, director of veterinary services for the Cats Protection charity, said West Ham's decision to select Zouma "sends an appalling message to fans and the wider public".
The reaction has also been strong in France, with animal rights groups condemning Zouma's behaviour.
The SPA animal welfare charity said the defender should never play for France again in a letter to the French Football Federation seen by AFP.
Source: France 24
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