A 20-year-old man suffered a knife wound to the leg during the fight inside the shop on Saturday evening.
Video footage shared on social media captured part of the confrontation as a mannequin and other objects were thrown on to the floor.
One youth was seen holding a knife in his right hand down by his side as he faced a group of men walking towards him.
Repeated shouts of "no" can also be heard as the group moves through the store.
The injured man was taken to hospital for treatment before being arrested on suspicion of affray.
Seven others, including six men aged between 18 and 26 and a 20 year-old woman, were arrested on suspicion of GBH and affray.
The Metropolitan Police are appealing for witnesses.
"Officers were called at approximately 19:35hrs on Saturday, 8 May to reports of a fight at Selfridges in Oxford Street," the force said in a statement.
"On attending the location, officers found a man, aged 20, with a stab injury to the leg. He was taken to hospital for treatment before being discharged. He was subsequently arrested on suspicion of affray and remains in custody.
"Seven other people have been arrested on suspicion of GBH and affray. All remain in custody at this time."
The incident is being investigated by detectives based at Westminster.
To provide information contact police on 101 or tweet @MetCC and quote CAD 6085/8May, or contact the independent charity Crimestoppers anonymously on 0800 555 111.