Odegaard scored three goals and provided three assists either side of the World Cup break.
He is the second Norwegian after Erling Haaland to win the award and the first Arsenal player since Pierre-Emerick Aubameyang in September 2019 to do so.
Odegaard came out on top in an eight-man shortlist that included Haaland, Ben Mee, Joao Palhinha, Casemiro, Marcus Rashford, Kieran Trippier and Bukayo Saka.
Odegaard told the Arsenal website: 'It feels great. I've said a lot of times this team has a lot of young, hungry players and we play so well with each other, so it's just a pleasure to be here and to be part of what we're doing now.
'It's a pleasure to play with them and show my qualities so I'm very happy to get this award.'
Arteta took home the managers' honour after leading Arsenal to emerge victorious in all four games during the specified period.
Arteta beat fellow nominees Jurgen Klopp, Thomas Frank and Eddie Howe to the award.
It is the second time the Spaniard has won the award this season and his fourth overall.
