Moyes was criticised for picking Zouma in Tuesday's win against Watford after a video emerged of the French international kicking and slapping his cat.
National League club Dagenham and Redbridge have suspended Zouma's brother Yoan, who is understood to have filmed the video.
But Moyes has refused to change his mind and Zouma remains in contention to play for the Hammers at the King Power Stadium this weekend.
"Yes he's available to play against Leicester," Moyes told reporters on Friday.
"There are different views and opinions on should he be available. We as a club took that decision and I stand by that."
West Ham strongly condemned Zouma's actions earlier this week and fined him the "maximum amount possible" -- reported to be two weeks' wages totalling around £250,000 ($340,000).
Zouma had issued an apology, but the 27-year-old lost his deal with sportswear giant Adidas over the disturbing video.
As well as hitting the cat, the footage also saw Zouma throw a shoe at the animal while laughter was heard in the background.
Insurance and investment company Vitality announced it was suspending its sponsorship as West Ham's "official wellness partner", saying it was "distressed" by the video.
Aware of the widespread condemnation of Zouma and the anger sparked by his selection on Tuesday, Moyes was adamant the club had done all they could to remedy the situation.
He revealed Zouma will be given education on animal welfare by the RSPCA.
'Terrible and diabolical'
"I don't think the club could take more action or any quicker. West Ham have fined him the maximum wages. We all accept the actions are terrible and diabolical," Moyes said.
"We are so disappointed it is completely out of character from Kurt. He is a really good lad we are going to get him some help and trying to give him as much help as we can.
"Like drink-driving offences, most people have to go to classes and the RSPCA are going to provide him with classes.
"We will do everything we can to make sure Kurt is looking into it, and getting better, and understanding it."
The RSPCA and Essex police are working together to investigate the incident, with the animal charity taking Zouma's pet to check on its well-being.
Around 200,000 people have signed an online petition calling for Zouma to be prosecuted.
Moyes has not been afraid to drop players for disciplinary reasons, having previously left Michail Antonio out for being late for team meetings.
But on Zouma's continued presence, the former Manchester United boss said: "He's treated the exact same way as any other player.
"I've never had an incident like this. That's part of being in this job.
"We'd rather we weren't making news. West Ham have made really good news in the last two years.
"We've a really good side. I'm sad the focus has been taken away from what is, at the moment, a really good season."
