In the other two ties, last season's finalists Liverpool were drawn against Porto, while Real Madrid's conquerors Ajax will face Juventus in a rematch of the 1973 and 1996 finals.
United and Barcelona have met twice in the final, in 2009 and 2011, with the Catalan giants winning on both occasions.
Champions League quarter-final fixtures
Ajax vs Juventus
Liverpool vs FC Porto
Tottenham vs Man City
Barcelona vs Man Utd
Matches to be played across April 9-10 and April 16-17
Champions League semi-final fixtures
Ajax or Juventus vs Tottenham or Man City
Barcelona or Man Utd vs Liverpool or FC Porto
Matches to be played across April 30, May 1 and May 7-8
When is the final?
The final takes place on June 1 at Atletico Madrid's Wanda Metropolitano Stadium.
Confirmation of fixture dates
Quarter-final first-leg dates
Tuesday 9 April: Liverpool vs Porto, Tottenham vs Manchester City
Wednesday 10 April: Manchester United vs Barcelona, Ajax vs Juventus
Quarter-final second-leg dates
Tuesday April 16: Barcelona vs Manchester United, Juventus vs Ajax
Wednesday April 17: Porto vs Liverpool, Manchester City vs Tottenham
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