About 1,000 people watched the Queen's Gurkha Signals parade in Nuneaton on Sunday to mark the unit being given the Freedom of the borough.
The arrests happened when the English Defence League clashed with officers as they were ordered to disperse, police said.
The force is now studying CCTV footage as part of its investigation.
'Minor disorder'
Ch Insp Adrian Knight, from Warwickshire Police, said the Gurkha parade itself passed off without incident.
"Post parade there were several incidents of minor disorder which were dealt with," he said.
"Arrests were made but it was an appropriate and proportionate response from police."
Nuneaton and Bedworth Borough Council awarded the Freedom of Entry to the regiment - the highest honour a council can award to a serving unit of the armed forces.
The Second Battalion, The Royal Regiment of Fusiliers, was presented with Freedom of Entry to the borough earlier this month.
BBC