Thw 22-year-old Wales international scored five times in five games in September, including a brace in the 3-1 victory at Sunderland.
Meanwhile, Gunners boss Arsène Wenger was named the Premier League manager of the month following a run of impressive form which has seen his side top the table.
The Frenchman guided Arsenal to six victories in six matches, leaving the Gunners top of the Premier League heading into the forthcoming international break.
Wenger, 63, has now won 13 Premier League manager of the month awards since his arrival at Arsenal in October 1996.
Arsenal currently top the table with 16 points from seven games following Sunday’s 1-1 draw at West Bromwich Albion.
Asked about his side’s chances of winning their first Premier League title since 2003-04, Wenger said on Sunday: “A mentality of being champions is built up through the season and I believe that we continue to focus on the way we want to play.
“We have desire, we have the spirit but we are only in October, in March and April you can show that you have the mentality of champions but at the moment it’s early and it’s good to continue our run.”
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