The two men were on one of five bus loads of supporters who had travelled to support Kidderminster Harriers against Luton Town FC.
Police said that as the coaches queued in traffic about a mile from the Kenilworth Road ground an argument broke out between "local residents" and supporters.
Four local men have been arrested and police are investigating the violence which broke out in Dunstable Street near the Mansfield Road junction.
More top news
An inquest is to be opened into the death of ex-Aston Villa footballer Dalian Atkinson after he was shot with a police Taser.
Detectives leading a criminal investigation into the disaster want to speak to 19 people seen on CCTV at the stadium that day.
Feeling muggy tonight but remaining dry.