Twenty males were arrested on suspicion of violent disorder or affray after the fight in Price Street, Birmingham, at 16:15 GMT on Saturday.
Police said eight Villa supporters and seven Leicester fans were held after trying to run away from officers.
Five more were arrested after being found hiding in a nearby car park.
West Midlands Police said the fans were aged between 16 and 21 and had been bailed until dates in February and March.
Insp Richard Vickers said: "These few individuals who choose to display their 'support' through anti-social or criminal activity are dealt with strongly and we will always push for Football Banning Orders against such offenders."
The match ended in a 1-1 draw.
Football fans hurled bricks and bottles at each other in a "violent clash" before Aston Villa played Leicester City.