Thirteen football fans were arrested as trouble broke out after Leicester's home tie with Norwich.
Officers were called to reports of fighting between rival groups of supporters at Loseby Lane on Saturday. Some men sustained minor injuries.
A police spokesperson said nearby buildings were also vandalised by fans who were throwing objects around.
Supt Chris Rollings said a full investigation was under way. The Foxes won the Championship fixture 4-0.
'Stamp out disorder'
"We believe a number of fans left the football ground early and made their way into the city centre.
"My officers responded quickly to the incident and a short while later a number of people were arrested.
"The majority of fans are law-abiding and peaceful and just want to enjoy the match and support their team and we are determined to stamp out disorder such as this, caused by a small minority, said Supt Rollings.
Officers have appealed for witnesses to come forward.