Moore has cemented a place at the heart of the Foxes defence this season and his side went unbeaten in the month, while he grabbed his first career goal in the 2-0 win over Wigan.
Moore said: "It is very nice. It is something I will be able to keep forever and it's an achievement.
"But if it's personal success or team success then I will pick team success every day. If they both come together then I couldn't be more grateful."
Leicester boss Nigel Pearson said: "Liam has had a very good start to the season - and he did last year. As a young player he has developed very well.
"He has worked exceptionally hard. He is playing alongside experienced players and experienced players can sometimes be the best coaches.
"It's great for him to pick up an award as an individual but he would be the first to recognise that to win awards like that you have to be part of an effective team and he has contributed very well so far."