Jose Mourinho's side progressed to the next round of the competition courtesy of a 4-0 aggregate win over Saint-Etienne on Thursday night and will now face the Russian Premier League runners-up over two legs next month.
Elsewhere, Gent's reward for knocking out Tottenham Hotspur is an all-Belgian tie with Genk, while Schalke will face off against Bundesliga rivals Borussia Monchengladbach and French side Lyon will take on Serie A outfit Roma.
The ties will be played on March 9 and March 16.
Europa League last 16 draw in full:
Celta Vigo vs. Krasnodar
APOEL vs. Anderlecht
Schalke vs. Borussia Monchengladbach
Lyon vs. Roma
Rostov vs. Manchester United
Olympiacos vs. Besiktas
Gent vs. Genk
Copenhagen vs. Ajax