The Londoners were paired with the Swiss league leaders in the semi-final draw at UEFA headquarters, with Fenerbahce taking on Benfica in the other tie.
Chelsea, who beat Rubin Kazan 5-4 on aggregate in the last eight, will play the first leg in Switzerland on April 25 before hosting Basel at Stamford Bridge a week later.
Basel are competing in their first European semi-final but Thursday's penalty shoot-out defeat of Tottenham came on the back of victory over Zenit St Petersburg in the previous round.
The tournament is guaranteed a new winner this year and Fenerbahce are also novices at this stage of European competition.
Benfica and Chelsea have both won the continent's top prize, but neither have a UEFA Cup or Europa League on their CV.
Of the two Benfica have come closer, losing 2-1 on aggregate to Anderlecht in the 1983 final.
Chelsea boss Rafa Benitez said: "Everyone could be difficult but Basel is not too far away, so maybe it is a good option. We know Basel have a great atmosphere in their stadium, so it will be interesting."