The Argentinian, who was stripped of the captaincy last season amid a long contract dispute, has been linked with a possible move to Juventus.
Icardi was the joint top-scorer in the 2017-18 Serie A campaign with 29 goals, but managed just 11 last term having spent 53 days on the sidelines after being replaced as skipper by goalkeeper Samir Handanovic.
"@MauroIcardi will today return to Milan from our training camp in Lugano," Inter said on Twitter.
"The club and the striker have come to this decision by mutual agreement. Icardi will continue his pre-season training over the next few days and will take no part in our summer tour of Asia."
Inter Milan endured a topsy-turvy campaign last season, only securing fourth place and Champions League qualification on the Serie A final day.
Luciano Spalletti left his role as head coach in May, with former Juventus, Italy and Chelsea boss Antonio Conte taking over.
They have already been busy in the transfer market, bringing in experienced centre-back Diego Godin from Atletico Madrid on a free transfer and signing Italy midfielder Nicolo Barella from Cagliari.