Sainsbury's Local in Waterloo Road was sealed off by police on Monday evening after a youth was assaulted at the mini supermarket.
Police were called to the store – opposite Waterloo Station – just before 4pm on Monday.
A Scotland Yard spokeswoman said: "Officers and the London Ambulance Service attended and found a male youth with a cut to his face.
"He was taken to a south London hospital with injuries not thought to be life threatening or life changing.
"Two youths were arrested for grievous bodily harm close to the scene in Stamford Street. They currently remain in custody pending further inquiries."