Shakhtar Donetsk will play Olympique Marseille and Dynamo Kiev face Paris St Germain with the winners lined up to meet in the semis after the draw was made by UEFA on Friday.
No Ukrainian side had ever previously made it to the UEFA Cup last eight.
Werder will be at home first against Italy's last European contenders Udinese in their quarter-final tie.
City, the world's richest club following their takeover by Abu Dhabi United Group last year, needed penalties to beat Denmark's Aalborg in the last round.
England's last remaining representatives will come up against former Tottenham Hotspur boss Martin Jol, who is now in charge of Bundesliga high-flyers Hamburg.
The semi-finals take place on April 30 and May 7 with the final set for Wednesday, May 20 at Fenerbahce's stadium in Istanbul.
