The video which was posted on Snapchat on Sunday afternoon shows Zouma kicking the cat across his kitchen floor and slapping it in the face.
The disturbing video has been condemned by animal welfare charity Royal Society for the Prevention of Cruelty to Animals(RSPCA).
"This is a very upsetting video. It's never acceptable to kick, hit or slap an animal, for punishment or otherwise," an RSPCA spokesperson 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."
West Ham have also taken issue with Zouma’s actions and will conduct an internal investigation.
A West Ham statement said: "West Ham United unreservedly condemns the actions of our player, Kurt Zouma, in the video that has circulated.
"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."
The France international has now issued an apology for the incident and outrage it has caused.
"I also want to say how deeply sorry I am to anyone who was upset by the video," he said. "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."
