Images shared on social media showed men hitting, kicking and hitting each other with suitcases at the airport around 8 a.m.
Other passengers could be heard shouting “stop” as the group collided in the airport waiting area.
Seventeen people were arrested.
Police are investigating the fight and the airport has apologized to the other passengers who were affected.
Bedfordshire Police said: ‘Police have been made aware of a violent disorder at London Luton Airport.
“Four people were injured and three were taken to hospital with serious injuries.
“Subsequently, 17 people were arrested and remain in custody for questioning.”
Luton Airport said: “We are shocked and saddened by this isolated incident.
“We take a zero tolerance approach to violence and continue to assist police with their investigations.
“We would like to apologize to all affected passengers.”
Images of the incident posted on Twitter showed a man wielding a knife in front of shocked shoppers in the Oxford Street department store.
Another man threw a dummy on the ground before two men started to fight.
The clip then showed the group heading to another part of the store under security guards.
A Met Police spokesperson said the injured man was stabbed in the leg and was not seriously injured.