Video from newspaper Aftonbladet shows the crowd shouting and running away from an advancing group of several police officers in Stockholm's downtown Sergel's square.
The newspaper reported police said the group is believed to have connections to local football hooligan organizations.
The group also handed out leaflets with the title "Enough already" that stated they were fed up with the "North African 'street children' raging around the capital's main railway station" and called on Swedish men to "defend our public areas for the imported criminality."
Although the exact number of people in the group remained unclear, the leaflet said it concerned "200 Swedish men."
Stockholm police spokeswoman Towe Hägg confirmed to Swedish Radio in Stockholm that the leaflets urged others to carry out crimes against youths but said police had so far not received any reports of violence against unaccompanied refugee children or other people with a foreign backgrounds.
Hägg said a plainclothes officer was punched in the face about 8:30 pm and the assailant was arrested for assaulting a police officer and violent resistance.
Three other individuals wearing masks and shouting were arrested for disturbing the peace.
Hägg said people with information in connection with Friday night's events should get in touch with the police.