Jose Mourinho's side were paired with the Spanish side in today's draw in Switzerland after their dramatic extra-time victory over Anderlecht in the last eight.
Ajax will face Lyon in the other semi-final.
All four semi-final ties and the final will be exclusively live on BT Sport, with the matches also available to stream on BTSport.com and via the award-winning BT Sport App.
The draw in full
Ajax v Lyon
Celta Vigo v Manchester United
When will the ties be played?
First legs: Thursday 4th May
Second legs: Thursday 11th May
Where will the games be shown?
Every single Europa League semi-final game will be shown on BT Sport on TV, as well as on BTSport.com and the BT Sport app.
And if you’re not yet a subscriber to BT Sport – the only place showing Champions League, Europa League, Premier League and FA Cup matches this season – we can get you set up in just 15 minutes right here.