Britain's other representatives face no lesser tasks, Celtic pitched against Italian champions Juventus and Arsenal with last season's runners-up Bayern Munich.
United's clash with Real - which will see Cristiano Ronaldo face his former team - was the pick of the ties, and Sir Alex Ferguson's men have the advantage of playing away first.
Ronaldo scored 118 goals in 292 appearances for United, but it was another Ronaldo - the Brazilian striker - who took the honours when the clubs last faced each other in 2003.
He scored a hat-trick at Old Trafford as Real went through 6-5 on aggregate.
Cristiano Ronaldo's last match for United was in the Champions League final defeat by Barcelona, after which he moved to Madrid for a world record £80m transfer.
United will play the first leg at the Bernabeu on February 13 with the return at Old Trafford on March 5.
Arsenal and Celtic, who were group runners-up, will both play their second legs away.
Arsenal will play the first leg at the Emirates Stadium on February 19 and the second at the Allianz Arena in Munich on March 13.
Celtic will take on Juventus at Celtic Park on February 12, with the return leg in Turin on March 6.
Barcelona, the bookies' favourites, will take on seven-time winners AC Milan and Borussia Dortmund, who many pundits are tipping to win the competition this season, will face the improving Ukrainians Shakhtar Donetsk.
Turkish champions Galatasaray will face Schalke, Valencia face Zlatan Ibrahimovic's PSG and Porto take on unfancied Malaga.
Galatasaray v Schalke 04
Celtic v Juventus
Arsenal v Bayern Munich
Shakhtar Donetsk v Borussia Dortmund
AC Milan v Barcelona
Real Madrid v Man Utd
Valencia v PSG
FC Porto v Malaga
First legs to be played 12/13/19/20th February, 2013
Second legs to be played 5/6/12/13th March, 2013