The 38-year-old retired in 2012 after 13 years with the Italian giants before moving into the backroom staff.
Inter paid tribute to Cordoba and confirmed his departure by mutual consent in a club statement.
"FC Internazionale and Ivan Cordoba announce that they have mutually agreed to end their working relationship. FC Internazionale would like to pay tribute to an unforgettable player and a great man. We wish him all the best for the future," it read.
Cordoba won multiple trophies at the club, including the 2009-10 Champions League.