Granada – who are in European competition for the first time in their history and eliminated Napoli in the previous round – will face Norwegian outfit Molde, who reached this stage by eliminating Hoffenheim at the previous stage.
Villarreal, who are regulars at this stage of European competition, eliminated Red Bull Salzburg in the previous round and are now paired up against Ukrainian giants Dynamo Kiev, who lost twice earlier this campaign against Barcelona.
The first legs will be played on 11 March, and the second legs will be played on 18 March.
Round of 16 Europa League draw:
Ajax v Young Boys
Dynamo Kiev v Villarreal
Roma v Shakhtar Donestk
Olympiakos v Arsenal
Dinamo Zagreb v Tottenham
Manchester United v Milan
Slavia Prague v Rangers
Granada v Molde