Louis van Gaal’s men, eliminated from the Champions League last week, were handed the tie in the draw for the last 32 of the second-tier competition at Uefa headquarters in Nyon.
Premier League rivals Liverpool were paired with German outfit Augsburg, while Tottenham were handed a rematch against their conquerors last season, Fiorentina. Gary Neville’s Valencia were drawn against Rapid Vienna.
United found themselves in the Europa League after finishing third behind Wolfsburg and PSV Eindhoven in their Champions League group. It is the second time in four years they have suffered such a fate. Their former defender Rio Ferdinand described their demise as “embarrassing” last week.
Midtjylland, who beat Southampton earlier in the competition, will host United on Februrary 18 and visit Old Trafford the following week.
Spurs avoided sides eliminated from the Champions League, but will face a stern test against Fiorentina, who are flying high in second in Serie A. The Florence side beat Spurs 3-1 on aggregate at the same stage last season, although it took two goals in the second half of the second leg in Italy to end the tie.
Liverpool may be happier with their draw, with Augsburg currently 13th in the Bundesliga, while Anfield boss Jurgen Klopp will undoubtedly relish facing opposition from his homeland.
Augsburg coach Markus Weinzierl was delighted to be coming up against Klopp and the five-time European champions.
Weinzierl said at a press conference: “The anticipation of facing Liverpool is huge. Everyone was happy.
“Liverpool are a cult club and Jurgen is a huge name in Germany so I’m happy for the whole club.
“We will do everything we can. This game is something special.”
New Valencia boss Gary Neville missed out on a reunion with former club United, with the Spaniards instead facing Austrian opposition.
“On paper Rapid is not the hardest tie but we’re taking nothing for granted,” said Juan Cruz Sol, Valencia representative.
“[Gary] Neville needs to grow little by little, and we have every confidence in him. Valencia’s fans know about football. We have a new boss and the fans know they need to be patient.”
Other notable ties in the round include Borussia Dortmund v Porto, Villarreal v Napoli, Sporting Lisbon v Bayer Leverkusen and Galatasaray v Lazio. Holders Sevilla, back in the competition after exiting the Champions League, face Norwegians Molde.
Meanwhile Manchester United midfielder Juan Mata expects the club to get through their “bad streak” following defeat at Bournemouth at the weekend, coming on the back of their Champions League exit at the hands of Wolfsburg.
“All I really want now is to have another game to play as soon as possible. But everything passes and this bad streak will pass,” said Mata in his club column.
“When we were coming back from Bournemouth all I could think about was the frustration of the defeat, the disappointment of those who came with us, those who watched the game on TV, those who were with us in Germany... and the only thing to turn that anger into happiness is through good results, not words.”