The tie will see United and France midfielder Paul Pogba, the world's most expensive player, come up against his elder brother Florentin, the Guinea international defender.
Mkhitaryan breaks duck as United go through
The teams met in the now defunct Cup Winners' Cup first round in 1977, with United winning 3-1 on aggregate.
On that occasion, United were forced to host the second leg in the southern English city of Plymouth, 450 kilometres away, following crowd trouble in the first leg in France.
Mourinho demands United improvement
Mourinho's men finished second in Group A behind Fenerbahce while Saint-Etienne topped Group C.
The other Premier League representative, Tottenham Hotspur, will face Gent of Belgium after being eliminated from the Champions League.
Villarreal of Spain will face Italian giants Roma in one of the standout ties, while Bundesliga club Borussia Moenchengladbach were drawn against Fiorentina of Italy.
The first legs will be played on Thursday, February 16, with the return matches a week later.
Here is the complete list of the draws.
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