Manchester United were rewarded for reaching the Champions League quarter-finals by being handed a daunting meeting with defending champions Bayern Munich.
The task facing David Moyes' side will be even harder after they were also drawn to play the second leg in Munich.
Jose Mourinho's Chelsea will face Paris St Germain, but will have the second leg at Stamford Bridge.
Real Madrid will face Borussia Dortmund while there is an all-Spanish meeting between Barcelona and Atletico Madrid.
Draw for the Champions League quarter-finals is as follows:
Barcelona v Atletico Madrid
Real Madrid v Borussia Dortmund
Paris St Germain v Chelsea
Manchester United v Bayern Munich
First-leg ties to be played on 1 and 2 April, with the second legs being played on 8 and 9 April.
Meanwhile, Italian champions Juventus will face Lyon in the quarter-finals of the Europa League as they bid to keep alive the dream of playing in the final at their home stadium.
Last year's beaten finalists Benfica, top of the Portuguese Liga, have been partnered with AZ Alkmaar, whose performances to date in the Europa League have provided some relief from a difficult campaign which has left them down in seventh in the Dutch Eredivisie.
Basle, who reached last year's semi-finals, must beat Spanish side Valencia in order to repeat what was their best-ever run in European competition, while the final tie is an intriguing match-up between Porto and Sevilla.