The 18-year-old, who has burst onto the scene with a string of impressive displays this season, won the club's official Player of the Month award for October.
"I will try to contribute to the team whenever I play and hopefully play my part in a successful season," he told the club's official website.
"I'm really pleased to win this award, especially as it is voted for by the fans, who have been very supportive of me. So, thank you for voting for me.
"It's good to be recognised for your performances on the pitch but I realise that I have to work hard and keep progressing as a player."
Januzaj recently signed a new contract at Old Trafford.