Boateng is reported to be facing between four and six weeks out as a result, with Germany's first World Cup game taking place on June 17 against Mexico in Moscow.
Taking to his official Twitter account, Boateng wrote: "Life is full of setbacks. Live, feel, love, laugh, cry, play, win, lose, stumble, fall, but stand up again and again. Now it is time to fight to be in Russia. I'll give it [my] all.
"For the remaining games this season I will support my team as well as it goes. Thanks for the many recovery wishes!"
Bayern also confirmed the nature of the injuries suffered by Arjen Robben and Javi Martinez during Wednesday's game.
Robben was replaced after eight minutes and has sustained an injury to his groin, "triggered by a muscle disorder".
Martinez made way 15 minutes from time due to a head injury and has suffered bruising.
While the Spain international has been ruled out of training for the next two days, no such confirmation has been made for Robben.