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 will face German outfit Augsburg while Tottenham were paired with Italians Fiorentina.
Gary Neville’s Valencia were drawn against Rapid Vienna.
The first legs of the ties are set to be played on February 18 or 25 with the return matches on March 10 or 17.
United have 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 dropped into the competition.
Spurs avoided sides eliminated from the Champions League but will face a stern test against Fiorentina, who are flying high in second place in Serie A.
Liverpool’s opponents Augsburg are not enjoying such a successful season, and are 13th in the Bundesliga, but manager Jurgen Klopp will undoubtedly relish facing opposition from his homeland.
Other notable ties in the round include Borussia Dortmund v Porto, Villarreal v Napoli, Sporting Lisbon v Bayer Leverkusen and Galatasaray v Lazio.
EUROPA LEAGUE ROUND OF 32 DRAW
Valencia v Rapid Vienna
Fiorentina v Tottenham
Borussia Dortmund v Porto
Fenerbahce v Lokomotiv Moscow
Anderlecht v Olympiacos
Midtjylland v Manchester United
Augsburg v Liverpool
Sparta Prague v Krasnodar
Galatasaray v Lazio
Sion v Braga
Shakhtar Donetsk v Schalke
Marseille v Athletic Bilbao
Sevilla v Molde
Sporting Lisbon v Bayer Leverkusen
Villarreal v Napoli
St Etienne v Basle
First legs to be played on February 18.
Second legs to be played on February 24/25.