The footage of French international defender Kurt Zouma has caused widespread condemnation and led to the RSPCA removing the animals from his home.
West Ham confirmed they had fined him "the maximum amount possible" and that the fee will be donated to animal welfare charities.
Zouma has since issued an apology over footage, saying there were “no excuses” for his behaviour.
Sportswear firm Adidas announced it had ended its deal with the 27-year-old and more than 150,000 people have signed an online petition calling for Zouma to be prosecuted.