The 39-year-old Spaniard lost all three games he played in August but bounced back with three straight wins in September.
Arsenal posted 1-0 wins over Norwich City and Burnley but it was their 3-1 victory over Tottenham Hotspurs in the North London derby at the end of the month that really caught the eye.
Arteta has emerged victorious in a five-man shortlist that also included Dean Smith, Graham Potter, Pep Guardiola and Jurgen Klopp.
"It's a great feeling, it means we went on a good run and won matches," Arteta said after picking up his award.
"But for me it's much more than that. It's about the people involved, the people who work with me and how grateful I am to have them.
"The level of trust, implication and passion that they show working alongside me every day, that gives me the strength and then the belief in the players that they can do it, and that they are good enough to win matches and that we believe in them."
Describing the club's home win against Spurs, he adds: "I said it after the game, it's the best atmosphere I've seen at the Emirates. It was electric, it was real, it was honest and it was a real sense of chemistry between our supporters and the team.
"And it was the perfect day to thank them. A few weeks earlier when we were under adversity and criticism they really stood for the team and it was a way for the team to say, 'Thank you, you are a big part of our time and we need you, and when you are alongside us look at what we can do.' "
Arsenal will host Crystal Palace after the international break.
