A police officer had to go to hospital with a head injury and a steward suffered a dislocated shoulder during disturbances at Burnley's friendly at home to German club Hannover.
Police said another steward was also hurt as trouble broke out in the Hannover fans' section at Turf Moor.
"The disorder we saw yesterday has no place in football," said police.
Burnley, who had been leading 1-0 after a header from Ben Mee, announced at half-time that the game had been abandoned.
In a joint statement, police and the club said that the injured officer has since been discharged from Burnley General Hospital. The steward with a dislocated shoulder is still in hospital.
Ch Supt Chris Bithell, of Lancashire Police, said: "A group of travelling Hannover fans, attempted to attack fans in the home stands, as well as police officers and stewards.
"Children and families were in attendance at what was a pre-season friendly match, which should have passed peacefully and without incident - but which ended up being abandoned due to the behaviour of some of the travelling Hannover fans."
He also appealed for fans with mobile phone footage of the disturbances to contact police.
Seats were ripped up and thrown after visiting supporters surged towards the home fans in the Cricket Field Stand about five minutes before the end of the first half.
Home supporters were moved from the stand as police moved in. The players did not appear for the start of the second half with the decision taken to abandon the match.
The statement from the club and police said "the behaviour of many Hannover fans before and during the game was confrontational from the outset".
It added: "Forty minutes into the game a large group of Hannover fans attempted en-masse to breach segregation and attack home supporters. This violence escalated with police officers and stewards being attacked and Lancashire police decided, in consultation with the referee and the club's ground safety officer, that the game could not continue.
"Extra resources were quickly drafted in from across the county and the visiting Hannover fans were escorted from the stadium and away from the ground to ensure no further disorder took place."
Burnley manager Sean Dyche added: "The referee came to see me and said he wanted us in the room just to get a feel for our general thoughts.
"I made it clear. It comes down to safety. The police decided to call it off and we support that.
"We understand that. It's important what the team do, but it's not as important as people coming to a football match. You want safety. You don't want people to get hurt.
"It's a shame what has happened but it's done, as simple as that.
"In the bigger picture I think the lads are fit and well. I think they've shown some good signs in pre-season and I think there's still more to come."
On Saturday night, Hannover released a statement condemning the behaviour of their fans.
"Our attitude is clear: Hannover 96 condemns the incidents in the stadium and dissociates itself vehemently from any kind of violence," the club said.
Burnley start their Premier League campaign away to champions Chelsea on 12 August.
Anybody with footage is asked to send it to Lancashire Police via https://doitonline.lancashire.police.uk/.