During the match, in which flares and other objects were thrown into the stands, a policeman was injured when a person from the away section threw a pyrotechnic device.
"Four Real Betis supporters were arrested for violent disorder, assault, possession of flares inside the stadium and possession of a controlled drug," Greater Manchester Police said in a statement.
"GMP are working closely with Manchester United, the UK Football Policing Unit, Real Betis, UEFA and colleagues from the Spanish Police to identify those involved in an ongoing post-match investigation," said Jamie Collins, chief inspector for the fixture.
Manchester Police added that two of the Betis fans arrested remain in police custody for questioning.
United won the first leg 4-1. The return fixture is scheduled for Thursday, which you can follow with Flashscore.
