Lazio and Fenerbahce, who have both been in trouble with UEFA over fan behaviour, were paired in another tie while Tottenham Hotspur, the only one of the quarter-finalists to have won the trophy, face FC Basel with the first leg in London.
Former European champions Benfica were drawn against Newcastle United, the third English Premier League side still in the competition. None are left in the Champions League.
"It's a great draw for us," Newcastle manager Alan Pardew said.
"The Estadio da Luz is a great venue. I've been there and it's a fantastic stadium. Importantly, we are at home in the second leg and that will give us an advantage."
Fenerbahce, at home in the first leg against Lazio, had to stage their last 16 second leg against Viktoria Plzen on Thursday behind closed doors after their fans set off fireworks during a previous home match against BATE Borisov.
Serie A side Lazio will play the second leg in an empty stadium in Rome as they complete a two-match sanction for racist behaviour Of fans, poor organisation and firework-throwing during the group stage match against Borussia Moenchengladbach.
It was Lazio's fourth racism offence this season.
The first legs will be played on April 4 and the second legs on April 11.
Europa League quarter-final draw
Chelsea v Rubin Kazan
Tottenham Hotspur v Basel
Fenerbahce v Lazio
Benfica v Newcastle United