The 27-year-old Frenchman showed no emotion as he was handed the sentence at Thames Magistrates’ Court in east London on Wednesday.
He drew international condemnation after footage emerged of him volleying the pet across his kitchen, before throwing a pair of shoes at it and slapping its head, saying: “I swear I’ll kill it.”
District judge Susan Holdham described the actions as “disgraceful and reprehensible”
Zouma pleaded guilty last week to two counts of causing unnecessary suffering to a cat, after blaming the family pet for damaging a chair.
Ms 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 but you caused unnecessary suffering for your own amusement.”
His two Bengal male cats have since been signed over to be rehomed.
The court was told the “premeditated” attack was filmed by his younger brother, lower-league footballer Yoan Zouma, 24, in February, and sent to a woman he was due to go on a date with.
But the woman was so shocked that she called off their meeting, telling him: “I don’t think hitting a cat like that is OK – don’t bother coming today.”