AC Milan had the better chances with Theo Hernandez scuffing wide and Samir Handanovic denying Rafael Leao.
The second leg - also at the San Siro, home of both teams - is on Wednesday, 20 April.
Before the game, a message from Milan and Ukraine legend Andriy Shevchenko on the big screen pleaded for an end to the war in his homeland.
"Italian friends, please make your voices heard... Ukrainians want peace because peace has no borders," he said to applause from the whole stadium.
Both Milan rivals are also competing for the Serie A title, with the top three - including leaders Napoli - only separated by two points.
Juventus and Fiorentina play in the other semi-final.
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