The versatile Croatia international Stanisic, who has a contract with Bayern until 2026 and can play in several defensive positions, was not in the squad on Friday for their 4-0 win at Werder Bremen in their league opener.
"In order to continue developing at the highest level he needs matches," Bayern CEO Jan-Christian Dreesen said in a statement.
"So we jointly decided on the loan to Bayer Leverkusen until next summer."
Coach Xabi Alonso's Leverkusen are seen as likely title contenders this season and won their opening match 3-2 against RB Leipzig on Saturday.