The Dutchman has not featured for the German champions since March 5 due to an adductor complaint, and will miss Saturday's DFB-Pokal final against Borussia Dortmund.
"I promise that I will return stronger than ever before," Robben was quoted as saying by AZ.
"It has been a very difficult time for me mentally.
"You always want to help the team as a player. It's the worst thing possible when you are forced to watch on from the sidelines.
"Next season is very important for me."
The 32-year-old scored seven goals in 22 outings for Bayern in 2015/16.