Icardi scored 20 goals in 31 games during the past season interrupted by the corona pandemic.
"The club thanks the player for the six seasons he was with us and wishes him the best in his future career," Inter writes in a statement.
Icardi has competed with Edinson Cavani for a place at the top of French champions PSG, but Cavani's contract expires this summer.
Argentine Icardi broke through in Italian Sampdoria before joining Inter where he was also the team captain.