The 27-year-old enjoyed a prolific spell in front of goal over the festive period, netting five times and providing one assist in five games for Pep Guardiola's side.
Sterling began December by assisting Ruben Dias's opening goal in a 2-1 victory at Aston Villa, before scoring City's first in a 3-1 win at Watford.
The England international then became the 32nd player in Premier League history to reach the 100-goal milestone when he converted from the penalty spot against Wolverhampton Wanderers to seal a slender 1-0 win on home soil.
City's number seven tapped in from close range to wrap up a comfortable 4-0 win at Newcastle United, before finishing 2021 with a brace in the enthralling 6-3 triumph over Leicester City on Boxing Day.
Reacting to his award, Sterling told City's official website: "I am delighted to win this award again – but December was an amazing month for the whole team.
"The Premier League is the most challenging competition in the world, so to win all seven of our league games throughout the month of December is incredible.
"Contributing to those wins with goals has felt good and that makes me happy. Hopefully we can continue this form because 2021 has been brilliant for us.
"All of us want to win trophies at the end of the season and that is what our aim will be from now until then."
Sterling wins the Player of the Month award for the third time in his career, after previously earning the prize in August 2016 and November 2018.