The Argentina international picked up a serious knee injury in the 2-0 win over CFR Cluj in the Europa League on Thursday night.
Despite the positive result, Stramaccioni said the injury "ruined the night" and expressed his support for Milito, who had only recently returned to the first team from another injury.
"Unfortunately, this injury rather ruined the night," the Inter coach told reporters.
"It is a lesion to the anterior cruciate ligament, damage to the collateral ligament and capsule. It is a terrible injury and totally new compared to the problems he had in the past.
"There's a one per cent chance of this happening, but it happened to Diego. We now just need to know when he'll have the operation. It's awful news, as we all care for him as a person as well as a player. I am personally very close to him and feel so sad right now."
Inter face Fiorentina in Serie A on Sunday.