The 27-year-old has also been banned from keeping cats for five years after pleading guilty to two counts of causing unnecessary suffering to protected animals at Thames Magistrates' Court.
Zouma's younger brother, Yoan, was sentenced to 140 hours of community service on Wednesday. The 23-year-old was suspended by his club, Dagenham & Redbridge FC, after the footage appeared.
Yoan filmed the incident involving the cat in February and posted it on Snapchat.
Kurt Zouma could be seen kicking his Bengal cat across his kitchen, before throwing a pair of shoes at it and slapping its head.
"Both of you took part in this disgraceful and reprehensible act with this pet cat," district judge Susan Holdham said.
"The cat looked up to you to care for its needs. On that date in February you did not provide for its needs."
West Ham fined Zouma two weeks of salary -- the maximum amount possible -- when the incident came to light, but manager David Moyes continued to pick the defender to play when fit. Zouma also lost a sponsorship deal with Adidas.
The Royal Society for the Prevention of Cruelty to Animals took Zouma's two pet cats into care after the incident.
The RSPCA brought the prosecution against the brothers even though it does not have the power to charge people.
British law allows organisations such as the RSPCA to use specialist lawyers to bring private prosecutions against individuals, with such cases heard in court and sometimes taken over by public prosecutors.
A West Ham spokesperson said: "West Ham United can confirm that Kurt Zouma has been handed a community service order following an investigation by the RSPCA.
"West Ham United wishes to make clear that we condemn in the strongest terms any form of animal abuse or cruelty. This type of behaviour is unacceptable and is not in line with the values of the football club.
"Within 48 hours of the footage emerging, we fined Kurt the maximum available to the club. Every single penny of this money is now with a number of deserving charities, all dedicated to animal welfare.
"Kurt admitted at the earliest opportunity that what he did was wrong. He has apologised without reservation.
"We hope that now the court has reached its decision, everyone will allow Kurt the chance to learn from his mistake and move on."
Information from The Associated Press and Reuters was included in this report.