West Ham have "unreservedly condemned" Kurt Zouma after a video emerged of the France defender kicking his cat across the floor and slapping it in the face.
Zouma, who has apologised, was named in the starting line-up for Tuesday's Premier League game with Watford.
Essex Police are liaising with the Royal Society for the Prevention of Cruelty to Animals (RSPCA) and say "urgent enquiries are ongoing".
The club have said they will deal with the incident internally.
West Ham boss David Moyes said of the decision to start Zouma in Tuesday's home game: "He is one of our better players. But it is ongoing and the club are dealing with it, so that is a separate matter."
In a statement, Zouma, 27, said: "I want to apologise for my actions. 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."
Further footage, first published by The Sun and reportedly filmed by Zouma's brother Yoan, shows the player throwing shoes at the pet and chasing it around a room.
"West Ham United unreservedly condemns the actions of Kurt Zouma in the video that has circulated," said the club, who signed the defender in the summer from Chelsea for £29.8m.
"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."
Yoan Zouma plays for Dagenham & Redbridge and the National League side said it "has had discussions with Yoan and we will now take some time to consider our response".
The club added: "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."
Yoan Zouma said: "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.
"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."
An Essex Police spokesperson said: "We are aware of a video circulating on social media relating to an incident involving a cat which members of our communities may find distressing.
"We have recently been made aware that this incident may have taken place in Essex and we are liaising with the RSPCA and urgent enquiries are ongoing."
The RSPCA said: "This is a very upsetting video and we'd like to reassure the public that we are investigating.
"We cannot comment further at this time but we're grateful to everyone who has brought this to our attention."
Kurt Zouma was also criticised by Professional Footballers' Association chief executive Maheta Molango as he gave evidence to a Digital, Culture, Media and Sport select committee 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," he said.
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