On Thursday, the centre-back who has been with the Bavarian since the age of nine was given a three-year deal.
Awoudja whose parents hails from Togo has gone through the ranks at Bayern and, last season, appeared 29 times in the Regionalliga, scoring four goals.
According to club sports director Hasan Salihamidzic, he is a ‘fast and strong centre-back’.
"We are very happy that Maxime stays with us. He's a fast and strong centre-back who has proven his potential in our amateurs and training sessions with the pros," Salihamidzic told club website.
Reacting to the feat, Awoudja said: "I'm just happy to have signed my first professional contract here at Bayern.
“Now I want to take the next step in my career. I know that I have to work at least as hard as before.”
The defender has appeared for Germany national youth sides but is still eligible to play for Togo.