The Blues, who dropped out of the Champions League at the group stages, have managed to avoid an all-Premier League clash against Tottenham Hotspur or Newcastle United.
Interim manager Rafael Benitez will take his side to Russia for the second leg on April 11 after trying to clinch a home advantage at Stamford Bridge on April 4.
Meanwhile, Tottenham will go up against Basel, while Newcastle have been drawn a two-leg tie with Benfica.
Europa League quarter-final matches:
Benfica vs. Newcastle
Fenerbahce vs. Lazio
Tottenham vs Basel
Chelsea vs. Rubin Kazan