The Magpies star's curling 25-yarder sealed a comeback victory at Molineux, nestling in the top right-hand corner beyond the hosts' goalkeeper Sam Johnstone.
It was the second of three goals scored by the former Leicester City winger during the month, with Barnes also on target against Tottenham Hotspur and Fulham.
He is on the shortlist alongside Aston Villa's Jhon Duran, Brentford's Bryan Mbeumo, Liverpool's Darwin Nunez, Arsenal's Riccardo Calafiori, Chelsea's Cole Palmer, Leicester City's James Justin and Everton's Dwight McNeil.
Magpies supporters can vote for Barnes by clicking here. The winner will be announced at 1pm BST on Friday, 11th October.