Gomez picked up the injury during Bayern's 4-2 penalty shoot-out defeat to Werder Bremen in the semi-final of the Liga-total! Cup on Saturday.
The 27-year-old will have loose fragments removed from his right ankle this week, according to a statement on the Bundesliga club's website, with no prediction as to when he will return to action.
"He is not very well," said Bayern's director of sport Matthias Sammer, who earlier announced the postponement of a friendly match on Wednesday due to his side's injury problems.
"He needs an operation. Then we will see how long he will be missing."
Gomez lasted just 42 minutes of the game against Bremen before limping off the field and he is unlikely to be fit for the start of the season, which commences on August 25.
