Jose Mourinho's side will face the Dutchman's Fenerbahce, as well as Feyenoord and Zorya Luhansk, a Ukrainian team who enter this stage of the competition for the first time in their history.
Southampton, the other Premier League side still in the competition, will play Inter Milan, Sparta Prague and Hapoel Beer Sheva.
Full draw:
Group A: Man Utd, Fenerbahce, Feyenoord, Zorya Luhansk
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Group B: Olympiacos, Apoel Nicosia, Young Boys, Astana
Group C: Anderlecht, St Etienne, Mainz, Qabala
Group D: Zenit St Petersburg, AZ Alkmaar, Maccabi Tel-Aviv, Dundalk
Group E: Plzen, Roma, Austria Vienna, FC Astra Giurgiu
Group F: Athletic Bilbao, Genk, Rapid Vienna, Sassuolo
Group G: Ajax, Standard Liege, Celta Vigo, Panathinaikos
Group H: Shakhtar Donetsk, Braga, Gent, Konyaspor
Group I: Schalke 04, FC Red Bull Salzburg, Krasnodar, Nice
Group J: Fiorentina, PAOK Salonika, Liberec, Qarabag
Group K: Inter Milan, Sparta Prague, Southampton, Hapoel Beer Sheva
Group L: Villarreal, Steaua Bucharest, FC Zurich, Osmanlispor