The Hammers had an opening for the armband after Declan Rice’s summer exit, with experienced heads such as Tomas Soucek and Aaron Cresswell tipped to take it up.
No official replacement has been announced however and Zouma, 28, has led the team out in their opening four Premier League games.
The defender has continued to impress on the pitch despite experiencing severe criticism off it, having been given a community service order after being filmed abusing his cat in February 2022.
“Kurt will continue as captain,” manager Moyes confirmed ahead of Saturday’s match against Manchester City.
“He’s done a good job, we’ve won three and drawn one of the opening four games, so he will continue in the role.”
West Ham host the treble-winners having enjoyed a fine start to the campaign, which Moyes described as coming despite a difficult schedule.
“We’ve had three of our four games away, which is a really tough call,” he noted.
“Quite a few have had three at home, so for us to get those points from three away games is really good. We’ve scored goals and we look as if we are going to score goals and if that continues we will have a great chance of picking up points.”