Footage of the incident has been widely shared on social media, showing an officer restraining a boy on the floor while onlookers shout at the police in the Mander Centre, Wolverhampton.
West Midlands Police said they were called after reports of two teenagers being abusive to shoppers and causing disorder at around 3pm on Monday.
The boys had reportedly gone missing from school and were taken into custody before being de-arrested. One of the boys also assaulted a police officer and damaged equipment at the police station he was taken to, the force said.
In the footage, an officer can be seen restraining the boy by resting his knee against the youngster's arm and holding him down.
In the video shoppers can also be seen protesting at police and accusing them of being heavy handed. A force spokesman said officers had to deal with "hostile" members of the public.
One person can be heard saying "he's only a child" while another says "look at the size of the little boy, you're a bully".
Chief Inspector Hasson Shigdar, from Wolverhampton police station, said that initial investigations showed that officers had "acted appropriately".
Police were first alerted by Mander Centre security.
A spokesman for West Midlands Police said: "We were alerted by the retail radio at the centre when two teenagers were causing a disturbance around 3pm after being reported missing from school.
"The boys were being abusive to shoppers and causing disorder.
"A PCSO attended but the level of behaviour by the boys was such that a plain clothes officer intervened and attempted to detain them.
"Additional officers were called for support and it was necessary to restrain a 13-year-old boy for his own safety and that of officers.
"Officers were also required to manage hostile members of the public while the boy and another 13-year-old were arrested for breach of the peace, during which one officer was punched several times.
"They were later de-arrested at the police station and handed over to appropriate adults.
"One of the boys will be dealt with at a later date for assaulting a police officer and damaging office equipment at the station."
Chief Inspector Hasson Shigdar, from Wolverhampton police station, added: "We understand that incidents like these are very emotive when viewed on social media, but please remember that a snapshot does not tell the whole situation the officers faced.
"We are collating bodyworn footage and our professional standards department will make a full assessment, but initial investigation shows that officers acted appropriately within Home Office guidelines."
A Mander Centre spokesman said: "An incident took place in the Mander Centre on June 14 and police attended.
"Centre staff followed the correct protocols to ensure the safety of staff and shoppers. The disturbance was dealt with by police officers and the matter is now in the hands of West Midlands Police.
"All enquiries concerning this incident should be directed to them to deal with.
"The safety of our staff and customers is taken extremely seriously and any incidents of disruptive and unlawful behaviour will always be dealt with as swiftly as possible by the relevant authorities."