The Ghanaian midfielder has scored nine times in 17 games in all competitions for the Hammers this season, alongside two assists.
He netted two goals in the 3-0 defeat of Wolves on Sunday.
Moyes has been impressed with how the former Nordsjaelland and Ajax player has adapted to the Premier League.
He said on Ghanasoccernet: "He's made a brilliant start here. I always say it's not easy for boys coming over from other leagues to do well in the Premier League initially.
"He's done great. He's all-round a really good player, and we're really thrilled."
Kudus will be missing for West Ham from January as he takes part in the Africa Cup of Nations in the Ivory Coast.