He was attacked in the lobby of Southfields Academy in Merton Road, Southfields, at about 15:10 GMT on Tuesday, police said.
Officers said they found three knives, and four teenagers have been arrested on suspicion of causing grievous bodily harm.
They remain in custody and inquiries are being made by officers based at Wandsworth CID.
A London Ambulance Service spokesman said an ambulance was sent to the school. The patient was treated at the scene and taken to a south London hospital as a priority.
A spokesman for the school said the boy was attacked by a group of teenagers who had no connection to the academy.
He said: "Our student suffered a stab wound to the leg and is being treated in hospital.
"Fortunately he is expected to make a full recovery and we are supporting him and his family in every way we can."
A 15-year-old boy has been stabbed in the leg at school in south-west London.