Some of the victims are said to have suffered stab wounds during the incident on Sunday afternoon.
Bedfordshire Police said they had been alerted to the fight in a residential street northwest of the town centre at 4.50pm.
The force tweeted: “We were called to Saxon Road in #Luton after receiving reports of a large number of individuals fighting.”
Emergency services took some people to hospital for medical treatment “after reports of stab wounds”.
Seven people were being treated in hospital and one was in a critical condition, the force said.
Police have appealed for witnesses of the incident to come forward and anyone with information can call the police on 101 quoting incident 299.