The Metropolitan Police said officers were called by the London Ambulance Service to Our Lady of the Annunciation Church in Croydon on Wednesday.
One adult was also reported to have received burn injuries which are not believed to be serious, police added.
The child has been taken to hospital and his next of kin have been informed.
A spokesman from the London Ambulance Service said: “We were called at 2.10pm today to reports of an incident on Bingham Road, Croydon.
“We dispatched two ambulance crews, an emergency responder, a medic in a car and an incident response officer to the scene. We also dispatched a trauma team from London’s Air Ambulance.
“We treated three people at the scene for burns including a child, a man and a woman.
“We took the child to hospital by air. We also took the man and the woman to hospital by road.”
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