It is the second time Rashford has won the award this season after also scooping it in September.
The 25-year-old scored three times in four games in January, finding the net against Bournemouth, Manchester City and Arsenal.
Rashford came out on top in a seven-man shortlist that included Brennan Johnson, David Raya, Dan Burn, Bukayo Saka, Riyad Mahrez and Solly March.
“It’s obviously a nice feeling [to win the award],” Rashford told MUTV’s Mark Sullivan.
“For me, we’re entering one of the most important parts of the season, so I’m still looking to achieve a lot of things. Winning these types of achievements along the way always helps you to push forward and improve.
“I’m hoping that I can continue to do that in the coming games.”
Elsewhere, Arsenal boss Mikel Arteta was named manager of the month.
Arteta beat Steve Cooper, Unai Emery, Roberto De Zerbi and Thomas Frank to emerge victorious.
It is the third time Arteta has won the honour this season.
Arsenal went unbeaten in January, beating Manchester United and Tottenham Hotspurs along the way.
"After the World Cup break, you have certain questions: how is the team going to react, are we ready and have we lost that momentum?" Arteta told the club's official website.
"I don't think we did, I think we used that time really well.
"It's difficult to choose the best moment because we had some big ones, but obviously the game that we won away at Spurs was a key one."
