The Magpies winger was in scintillating form for Eddie Howe's men throughout the month, netting three superb goals in four games.
Barnes' first-time finish in the 2-1 win over Tottenham Hotspur kicked off the month, and the 26-year-old followed up that strike with a stunning winner at Wolves midway through September.
He was also on target with a typically precise finish in the defeat at Fulham, and helped United come back from goal down to secure a draw against champions Manchester City.
Barnes in shortlisted for the award alongside Cole Palmer of Chelsea, Luis Diaz and Ryan Gravenberch of Liverpool, Dwight McNeil of Everton, Arsenal's Gabriel, Aston Villa's Ollie Watkins and Raul Jimenez of Fulham.
Newcastle fans can vote for Barnes by clicking here. The winner will be announced at 11am BST on Friday, 11th October.