The Red Devils defeated Barcelona 2-1 on Thursday to complete a 4-3 aggregate victory over the Spanish side.
A 5-1 aggregate win for Sporting over Midtjylland sees the Portuguese side face the Gunners.
Jose Mourinho's AS Roma side square off against Real Sociedad while Juventus are up against Freiburg.
Habitual winners Sevilla have been paired with Fenerbahce while Shakhtar Donestsk will face Feyenoord.
The first legs will take place on March 9 and the return legs are on March 16.
The final for this season’s Europa League will be held at the Puskas Arena in Hungary on May 31 2023.
Frankfurt are the current holders of the competition after beating Rangers on penalties at the Ramon Sanchez Pizjuan Stadium in Spain in May last year.
Europa League last-16 draw
Union Berlin v Union Saint-Gilloise
Sevilla v Fenerbahce
Juventus v Freiburg
Bayer Leverkusen v Ferencvaros
Sporting Lisbon v Arsenal
Manchester United v Real Betis
Roma v Real Sociedad
Shakhtar Donetsk v Feyenoord
