There have been calls for Moyes to drop the French defender over the video which emerged of him kicking and slapping his cat.
Moyes caused more controversy by picking Zouma to face Watford on Tuesday, barely 24 hours after the footage was released and amid a huge public outcry.
National League club Dagenham have suspended Zouma’s brother Yoan, who is understood to have filmed the video, while the RSPCA investigate the incident.
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Over 300,000 people have signed a petition calling for Kurt Zouma to be prosecuted for animal cruelty on petition site, Change.org.
But despite the calls, West Ham manager David Moyes confirmed the centre back remained available.
Speaking at the pre-match press conference he said: “Yes he’s available to play against Leicester. There are different views and opinions on should he be available. We as a club took that decision and I stand by that.”
Zouma has been fined the maximum two weeks’ wages, which will go to animal welfare groups.
Moyes added: “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.
“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.”
He added: “He’s (Zouma) treated the exact same way as any other player.
“I’ve never had (an incident) like this. As a football manager it shows you never know what you’re going to get.”
He added: “That’s part of being in this job. We’d rather we weren’t making news. West Ham have made really, 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.”