The 22-year-old, who has made 15 appearances for United this season, won the award for September as well.
But McTominay is focused on achieving success as a team with the Carabao Cup, FA Cup and Europa League in his sights.
“It’s pleasing to win a couple of individual trophies, it’s a nice feeling,” he told the club’s official website.
“But it’s difficult when we’ve had a lot of games. It’s a very, very busy period and three or four of the lads could have easily won it as well. So I was fortunate and I thank the fans for voting for me.
“The more important thing is that, when it comes to the business side of the season, we’re there or thereabouts and we can win things collectively as a group. That’s what everybody is dying for in that changing room.
“We could have three trophies this season and it’s something that we’re really looking forward to and aspiring to in terms of a group and our goals as well. It’s brilliant to win player of the month, but it’s about the collective and I wouldn’t be able to win it without my team-mates.”