Six arrests were made after scuffles broke out ahead of Manchester United's opening match of the Premier League season against visitors Leeds United, police said.
Fans were filmed hitting each other with chairs and bins on the streets of Manchester city centre on Saturday morning before the lunchtime kick-off, videos posted on social media showed.
Greater Manchester Police said that despite “isolated incidents of disorder” before kick-off, the match at Old Trafford passed “largely without police incident”.
Police said that six arrests had been made over the course of the day - five in relation to public order offences and one on suspicion of drug offences.
The force said that work was also under way in conjunction with football investigating officers from both Manchester United and Leeds United to identify people involved in other incidents of disorder.
In one video clip shared on Twitter, which appears to have been filmed from inside a coffee shop, someone can be heard saying “Good job we’re in here” as a large crowd runs through the street outside.
A member of staff appears to lock the doors to the premises as the men outside throw punches, chairs and bins at each other.
Two police officers armed with batons attempt to break up the crowd, which is quickly dispersed as a wailing siren draws near.
In another video, fans can also be seen brawling outside a pub before kick-off at Old Trafford.
Chief Superintendent Stuart Ellison said: "Despite isolated incidents of disorder in the city centre prior to kick-off, today's events at Old Trafford largely passed without police incident and I would like to thank the majority of the public for their cooperation throughout the day.
"Six arrests were made over the course of the day; five in relation to public order offences and one on suspicion of drug offences.
"These suspects remain in custody in cells in Greater Manchester for questioning this evening.
"Today was an important day for a lot of people with the return of capacity crowds at venues that have remained absent for such a long time, and I would like to thank the public, our officers and our partners from all agencies involved who helped make sure today was a safe and enjoyable affair for a vast majority of those concerned."
Manchester United ended up thrashing Leeds United 5-1 in the Premier League’s early kick-off on Saturday.