The 27-year-old France international has also been fined nearly £9,000 in court costs.
The Royal Society for the Prevention of Cruelty to Animals(RSPCA) started prosecution proceedings against the former Chelsea defender and his younger brother Yoan in March after a video emerged on social media of them maltreating a cat.
The video which was posted on Snapchat back in February showed the older Zouma kicking the cat across his kitchen floor and slapping it in the face while Yoan filmed it.
The RSPCA have since taken custody of Kurt's two cats.
Sentencing the brothers at the 15-minute hearing on Tuesday, the district judge Susan Holdham said: “Both of you took part in this disgraceful and reprehensible act with this pet cat.
“You must be aware that others look up to you and many young people aspire to emulate you.”
She added: “The cat looked up to you to care for its needs. On that date in February you did not provide for its needs.”
Following the verdict, a West Ham statement read: "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."
In a statement, RSPCA chief inspectorate officer Dermot Murphy said: "We hope this case will serve as a reminder that all animals deserve to be treated with kindness, compassion and respect, and that we will not tolerate cruelty by anybody."
