Having scored Bayern's first goal in the 3-1 victory, the playmaker had to be taken off during the first half at Allianz Arena after going down innocuously in the middle of the pitch.
Bayern confirmed after the game that the former Lyon man had torn his anterior cruciate knee ligament and would be set for several months on the sidelines.
Tolisso posted a tweet on Sunday to say he would be "back stronger" next year.
"I'll be back stronger, see you soon in 2019," the World Cup winner wrote.
The France international, who won the 2018 World Cup earlier this year in Russia, transferred to Bayern from Lyon last year for a fee of €41.5 million (£37m/$48m), a then-record purchase and sale for both clubs respectively.
The 24-year-old fast established himself as a key member of Jupp Heynckes’ team as they swept to the Bundesliga title and reached the final of the DFB-Pokal, making 32 appearances at domestic level and scoring seven times.
Tolisso was not the only injury Bayern sustained during the Bundesliga clash, with Rafinha suffering ankle ligament damage following a heavy challenge from Karim Bellarabi.