The striker returned to Bayern from Werder Bremen on a one-year deal last May and was pleased to be able to stay on under new boss Pep Guardiola.
The Peruvian told the club website: "I am 34 - I could think of nothing better than signing another contract at Bayern Munich.
"I am convinced we will have a good year together.
"What will happen in a year I can't say. But I feel very good and would like to play football for as long as possible."