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.
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Pre-match pictures from Twickenham as Wasps V Exeter match gets underway.
Very warm and humid with scattered thundery showers.
Very warm with sunny spells. Increasing risk of thunderstorms later.