There was nothing to suggest a collision in which six people were hurt near an English Defence League protest was deliberate, police have said.
The ambulance service was called to the incident in King Street, Dudley, at 1605 BST on Saturday.
West Midlands Police said initial witness accounts had suggested that a family car had become caught up in a small pocket of protesters.
No-one received life-threatening injuries in the incident.
A force spokesman said the investigation was in its very early stages.
He added: "Whilst trying to work its way clear the car collided with some of the protesters as they left the protest area."
Anti-fascist group Unite Against Fascism held a counter-protest against the EDL, which says it is against Islamic extremism in the UK.