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.
Experience Kissimmee, which has sponsored the London club since 2016, said in a statement on Wednesday (9 February) that “due to recent events” it had also cut sponsorship ties with the team.
“As an organisation and community, we welcome visitors and locals alike to join us in celebrating wildlife and nature, now and always. We are proud to work with partners who are accredited, certified and regulated to the highest standards of animal care,” said president and chief executive DT Minich.