The 30-year-old scored five goals in four league appearances for the Gunners last month, including a late free-kick winner against Aston Villa.
The Gabon international also netted a brace in a 2-2 draw against Watford and equalisers against Spurs and Manchester United.
Liverpool’s Jurgen Klopp was named manager of the month for the second consecutive month.
The Reds, who remain unbeaten at the top, beat Newcastle United, Chelsea and Sheffield United in September.
The German saw off competition from Bournemouth’s Eddie Howe, Chelsea’s Frank Lampard and Leicester City’s Brendan Rodgers.
The Gabon striker beat Trent Alexander-Arnold, Kevin de Bruyne, Son Heung-min and Riyad Mahrez to the award.