Zouma was filmed kicking and slapping his pet cat by his brother in a video that went viral online a few months ago.
The 27-year-old pled guilty to the charges and was sentenced by a judge on Wednesday.
During the sentencing, District Judge Susan Holdham said the brothers "took part in this disgraceful and reprehensible incident".
She stated to Zouma: "You kicked and slapped either the same cat or both of them – that cat looked to you to care for its needs.
"On that date in February, you didn't provide for its needs but caused unnecessary suffering for your own amusement."
"You must have been aware that others look up to you", she said.
"Many young people aspire to emulate you."