Police said they were called to Terminus Terrace in Southampton, on Saturday following reports of disorder.
Officers were told a number of people were involved, with tables, chairs and glasses being thrown.
A 61-year-old man, from Bursledon, Hampshire, was taken to hospital with facial injuries.
Hampshire and Isle of Wight Constabulary said it received reports of "violent disorder" at the junction between Terminus Terrace and Oxford Street at 18:05 GMT.
The force said it believed those involved had been at St Mary's Stadium and were making their way out of the city when the trouble occurred.
A late James Ward-Prowse penalty earned Southampton a point as they came from behind against Tottenham to draw 3-3.
Det Insp Tim Judd said: "This would have been a frightening experience for those who witnessed this incident.
"There would have been a lot of people out and about in the area enjoying their Saturday evening who suddenly found themselves at the centre of this disorder."
The force said the 10 people arrested on suspicion of violent disorder and other associated offences were:
* Four men from Waltham Cross, Hertfordshire, aged 22, 23, 25 and 27
* A 19-year-old man from Haringey, north London
* A 33-year-old man from London
* A 24-year-old man from Hoddesdon, Hertfordshire
* A 24-year-old man from King's Lynn, Norfolk
* A 19-year-old from Southampton
* A 31-year-old man from Bournemouth
All remain in custody and witnesses are being sought.