Golovin was one of the breakout stars of the 2018 World Cup and garnered him heavy interest from Chelsea throughout the summer.
But a move to the Blues did not materialise as Monaco came in with a late bid to secure a €30 million move from CSKA Moscow to the Ligue 1 side.
However, he did not feature in the Trophee des Champions last weekend when Paris Saint-Germain recorded a 4-0 victory over Monaco.
Monaco have now confirmed on their website that Golovin has a "sprained right ankle" that he sustained in training, with the player revealing the extent of the injury.
"I have an ankle injury, the operation is not required," Golovin told Sport-Express.
"The process of recovery will take about three-to-four weeks."
Monaco open their Ligue 1 campaign against Nantes on Saturday, hoping to improve upon their finish last season when they finished second but 13 points behind PSG.