Away fans threw flares and pyrotechnics inside Old Trafford, resulting in the injury to the police officer.
Greater Manchester Police (GMP) said four away supporters were arrested for “violent disorder, assault, possession of a flare inside the stadium and possession of a controlled drug”.
Two remain in police custody.
GMP said a group of about 50 Real Betis supporters engaged in disorder during United’s 4-1 win, but the “vast majority” of the 3,600 visiting fans were “respectful and well behaved”.
Chief inspector Jamie Collins said: “The violent disorder experienced does not reflect the majority of supporters attending this fixture who went just to watch the football on the pitch.
“Last night’s behaviour by the minority was totally unacceptable and quite shocking for the decent supporters who may have got caught up in this.
“We are also continuing to offer the welfare needed to support one of our colleagues who was injured as a result when trying to keep the public safe.
“GMP are working closely with Manchester United, the UK Football Policing Unit, Real Betis, Uefa and Spanish Police colleagues to identify those involved in a post-match investigation which is ongoing.
“If any supporters from Manchester United or Real Betis and those attending the game have any information or footage that can assist with enquiries, they are asked to contact Greater Manchester Police on 101 as soon as possible so we can bring those responsible to justice and also to seek, where possible, football banning orders.”