The 25-year-old was instrumental in his side's charge against relegation in the month, contributing three goals in five games as Russell Martin's side registered their first league wins since September.
"I'm absolutely delighted for Alex and I'm delighted for us because he's been excellent," said Martin. "He's given us a massive improvement in terms of end product, we all know he's capable of it, but he's starting to show it.
"It's down to the application he's giving us in both training and matches – he's been excellent since we took over. He's taken every bit of information on, some of his goals have been outstanding, but his general play has been outstanding too."
Gilbey - formerly of Wigan Athletic and Colchester United - added: "I'm over the moon to win the award and it's a really proud moment for me, I'm chuffed – now it's looking to build upon this and go again for the rest of the season.
"I'm thankful to the rest of the team as well, we've been really good of late and in December we were very good. It's time to build upon it now, win more games and climb the table."