"We are also aware of the allegations that have been made through the media about police conduct and we have appointed an officer to investigate these," it said.
Shahid Malik, 33, who sits on Labour's national executive and is a member of the Commission for Racial Equality, was hurt during an outbreak of violence on Monday night.
Mr Malik, who lives in Burnley and is the son of the town's deputy mayor, said he had been trying to stop the violence.
But he told the BBC he had been arrested by "very hyped-up" police in riot shields.
He said: "The riot shields were smashed in my face, causing four to five stitches above the eye, a black eye, lacerations to the arm, bruises on the back of the head, on the body and on the legs."
Mr Malik said he had fallen unconscious before being taken to hospital in handcuffs. He was later discharged.
A police spokeswoman said the skirmishes began when police officers asked groups of young Asian men in the Abel Street area of the town to disperse.
"When police approached one of the groups ... officers came under attack when missiles including stones were thrown at them," she said.
A Lancashire Police statement confirmed that a man had been arrested, "and injured during the course of his arrest".
It said police were arranging to interview the man - whose identity it did not confirm - as part of a fuller inquiry into the circumstances that led to his arrest.
"We are also aware of the allegations that have been made through the media about police conduct and we have appointed an officer to investigate these," it said.
A total of 22 people, both white and Asian, were arrested in the sporadic violence - mainly on public order offences.
But there was no repeat of the weekend riots that saw shops, cars and a pub set on fire.
BNP leader 'in Burnley'
Mr Malik said he hoped his arrest would not inflame tensions further, or lead to retaliatory attacks on officers.
"We don't want any trouble," he said. "The police are not the targets.
"The only winners in all of this are the BNP, the NF and the far right-wing who will capitalise on it."
He said Nick Griffin, the BNP leader in Oldham - scene of serious race riots earlier this year - was in Burnley on Monday, and had been an "unwanted presence".
"That's the kind of attention we don't need," Mr Malik said.
"My fear is we become a kind of magnet for some of the far-right groups who will come here to recruit."
Extra police
Police have appealed for calm and warned that "large numbers" of officers would remain on the streets throughout Tuesday.
The weekend's violence, which saw shops, cars and a pub set on fire, was said to be sparked by an alleged attack on an Asian taxi driver by a gang of white youths.
Some have complained that the police took to long to respond to the incident.