The holders will have home advantage for the second leg.
Sevilla beat fellow Spaniards Athletic Bilbao on penalties in the quarter-final.
In the other semi-final Villareal will be at home to Liverpool in the first leg.
Juergen Klopp's Liverpool came from 3-1 down on aggregate against Borussia Dortmund to win 5-4 with a goal in the last minute.
The first legs are on April 28 with the return games on May 5.
Basle stages the final on May 18.
Original source: Sevilla to meet Shakhtar in Europa semis