A police officer was dragged and kicked and another suffered a fractured eye socket in clashes with protesters outside Manchester United's ground.
Greater Manchester Police (GMP) said officers were "met with hostility" at Old Trafford and the Lowry Hotel in Salford before the team's match with Liverpool on Sunday.
The game was later postponed after about 200 fans entered the ground.
A 28-year-old man has been arrested in connection with the protests.
Fans had gathered outside the ground and the hotel, where the team was staying before the game, to protest against the Glazer family's ownership of the club.
Asked about the protest while on a visit to Hartlepool, Prime Minister Boris Johnson said he understood "people's strength of feeling" on football and club ownership, but he did not think it was "a good idea to have disruptive behaviour, demonstrations of that kind".
Sports minister Nigel Huddleston said in a tweet that while passions were "running high in football", there were "ways to protest and make your voice heard without hurting or endangering others".
GMP said six officers were injured in the "violent disorder", in which flares "were let off and bottles and barriers were thrown at police officers and horses".
A spokesman said as the situation escalated, additional officers had to be deployed and officers "had to be drawn in from neighbouring forces to assist".
Assistant Chief Constable Nick Bailey said the behaviour "shown at this protest was absolutely atrocious".
He said his officers had been "trying to do their job and facilitate a peaceful protest", but a section of those present "became hostile and aggressive... and forced entry to the football grounds, making it very clear that this protest was not peaceful and ruining it for the majority of protesters".
"Our officers tried to engage with protesters, but were met with violence and aggression which resulted in enforcement action being taken," he said, adding that enforcement was "a last resort, but in these circumstances it was deemed necessary".
Mr Bailey said the force was "reviewing all obtainable evidence and following all lines of enquiry available to us in order to identify the organisers of this protest, as well as those responsible for the officer assaults".
"If anyone has any information at all in regards to this... please do get in touch with police as soon as possible," he added.
Earlier, the Manchester United Supporters' Trust released a statement, urging the club's co-chairman Joel Glazer to engage with fans to avoid a repeat of the protest.