The Gunners beat Burnley, Norwich and Tottenham Hotspur consecutively and the victories saw Arsenal rise from bottom of the table to 10th.
Despite that, a weekend draw with Brighton was a stumbling point - but coming on 3 October, it did not factor in the award for last month.
“It’s a great feeling, it means we went on a good run and won matches,” said Arteta.
Arteta beat Brighton’s Graham Potter, Liverpool’s Jurgen Klopp, Manchester City’s Pep Guardiola and Aston Villa’s Dean Smith to the award.
Meanwhile, Cristiano Ronaldo won the Player of the Month after returning to Manchester United at the end of the transfer window. The forward scored three goals in two matches to help put the club in the top four, including two on his return to Old Trafford against Newcastle United.
Ronaldo won the award ahead of Liverpool’s Mo Salah, Chelsea’s Antonio Rudiger, Watford’s Ismaila Sarr, Manchester City’s Joao Cancelo and Newcastle’s Allan Saint-Maximin.
Fans and some pundits couldn’t believe that Salah, who scored his 100th Liverpool goal in September, didn’t win.
Former Leicester player and Match of the Day presenter Gary Lineker said on Twitter: “He’s been terrific, but @MoSalah should’ve won this….comfortably.”
And BBC journalist Emma Sanders added: “Salah not winning the Premier League player of the month when he’s been the best player on the planet for five weeks is… hilarious.”
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