The Red Devils could have faced Valencia - the club coached by their former captain Gary Neville - but they avoided the Spanish side and were instead handed a two-legged tie against the Danish Superliga outfit.
Meanwhile, Liverpool manager Jurgen Klopp faced a potential reunion with his former club Borussia Dortmund, but even though he will not be facing his old outfit, he will return to his homeland Germany to face Augsburg, whom Klopp has only lost to once in eight meetings.
Tottenham Hotspur - the only other English team in the competition - face a difficult knockout clash against Fiorentina, who will host the Premier League club before travelling to White Hart Lane for the return leg.
Neville's Valencia side, who also exited the Champions League last week, will face Rapid Vienna.
The first legs are scheduled to be played on February 18, with the return fixtures taking place seven days later.
Europa League last 32 draw in full:
Valencia vs. Rapid Vienna
Fiorentina vs. Tottenham Hotspur
Borussia Dortmund vs. Porto
Fenerbahce vs. Lokomotic Moscow
Anderlecht vs. Olympiacos
Midtjylland vs. Manchester United
Augsburg vs. Liverpool
Sparta Prague vs. Krasnodar
Galatasaray vs. Lazio
Sion vs. Braga
Shakhtar Donetsk vs. Schalke
Marseille vs. Athletic Bilbao
Sevilla vs. Molde
Sporting Lisbon vs. Bayer Leverkusen
Villarreal vs. Napoli
Saint-Etienne vs. Basel