It is the first time the two most successful teams in English history have been drawn together in European competition.
United have won the English title 20 times and the Champions League three times, compared to 18 and five for Liverpool.
Between the pair they have won 18 European trophies, including the Super Cup.
The plum tie of the round will see United, who have never won the competition, head to Anfield on March 10 before hosting the Reds at Old Trafford a week later.
Three-time former winners Liverpool last won the competition in its previous guise as the UEFA Cup in 2001.
In another single-country draw, former Manchester United full-back Gary Neville’s Valencia will take on Athletic Bilbao.
Holders Sevilla faced a kinder draw against Basel, where this season’s final will be held, but there was nothing kind about Borussia Dortmund being paired with Tottenham Hotspur.
DRAW
Shakhtar Donetsk (UKR) v Anderlecht (BEL)
Basel (SUI) v Sevilla (ESP)
Villarreal (ESP) v Bayer Leverkusen (GER)
Athletic Bilbao (ESP) v Valencia (ESP)
Liverpool (ENG) v Manchester United (ENG)
Sparta Prague (CZE) v Lazio (ITA)
Borussia Dortmund (GER) v Tottenham Hotspur (ENG)
Fenerbahce (TUR) Sporting Braga (POR)
Ties to be played on March 10 and 17
