The Argentina striker suffered a painful knee injury during the Nerazzurri's 2-0 win over Cluj and is not expected to return to action this season.
Upon hearing the news, El Shaarawy took to Facebook to send his best wishes to the Champions League winner, hoping that he will be back on the field before long.
“I want to wish Diego Milito good luck,” El Shaarawy wrote.
“I send a big hug. You are a true champion and I hope you come back playing soon!”
The 33-year-old is Inter's leading goalscorer this term with nine goals in 19 appearances.