Should Chelsea, the only Premier League side left in Europe, make it past the twice European champions, they will face either Barca or Milan in the semi-finals.
The West London club have confirmed they will play in Lisbon on Tuesday March 27 and host the Portuguese giants at Stamford Bridge on Wednesday April 4.
Chelsea have two former Benfica players in their squad, Brazilians David Luiz and Ramires. The Portuguese club are currently second in their domestic league, a point behind Porto, and emerged triumphant in the group phase during which they drew home and away with Manchester United.
Benfica also overcame a 3-2 first-leg defeat by Zenit St Petersburg in the first knock-out stage, winning 2-0 at the Estadio da Luz to secure their place in the quarter-finals.
Chelsea's chief executive Ron Gourlay claimed it was a decent draw for the club, especially with the second leg being played at Stamford Bridge.
He said: "It's a good one for us but it doesn't matter who you get at this stage. It was important to get the away game first and hopefully we can build the foundation from there. We're pleased.
"Ramires and David Luiz will know a lot about Benfica - we also know a lot about them because they topped Manchester United's group."
Defending champions Barca will face seven-times winners Milan, having already played them twice in the group stage.
They are on course to face bitter rivals Real Madrid in the final after the current Spanish league leaders were drawn against Cypriot minnows APOEL Nicosia and the draw for the semi-finals also kept them apart.
Bayern Munich, whose Allianz Arena home will host the final of this year's competition, will play Marseille in the quarter-finals, with the winner of that tie going up against either APOEL or Real in the last four.
Marseille assistant coach Guy Stephan, whose side left it late to overcome Inter Milan in the last 16, said: "It's going to be a very important tie that will weigh on the end of our season. We'll have the disadvantage of playing the first leg at home.
"But we have a strong case having already beaten a German club this season. And Borussia Dortmund lead the Bundesliga ahead of Bayern. We also showed against Inter that we had a lot of resources in the final minutes."
Bookmakers reacted to the draw by making Chelsea 8/1 fourth favourites to win the Champions League and they are 1/2 favourites to progress against Benfica, who are 6/4 to eliminate them.
The bookies offer even money that the final will pit holders Barcelona against deadly rivals Real Madrid.
The first legs of the ties will be played on Tuesday March 27 and Wednesday March 28, with the return legs on April 3-4.
The semi-final first legs are scheduled for April 17/18, with the second legs on April 24/25.
The final will be played at Munich's Allianz Arena on May 19.
APOEL Nicosia v Real Madrid
Marseille v Bayern Munich
Benfica v Chelsea
AC Milan v Barcelona
Marseille/Bayern v APOEL/Real Madrid
Benfica/Chelsea v AC Milan/Barcelona