Three people, including the child, were injured during the incident at Our Lady of the Annunciation Church in Bingham Road, Croydon, at about 2.10pm on Wednesday.
Pupils from St Thomas Becket Catholic Primary School in south London were attending the nearby church for a musical nativity celebration when the boy's costume came into contact with a lit candle.
A man and a woman were also taken to hospital by road.
London Fire Brigade assistant commissioner for fire safety Dan Daly said: "This horrific accident is a stark reminder of the risk real candles can pose.
"They are a completely unnecessary hazard when it comes to children and school plays.
"Sadly this isn't the first time we have seen clothing and costumes set alight by candles and people need to recognise the risk and prevent these incidents from happening again.
"People should not be using real candles - especially around children, costumes and decorations - when there are far safer alternatives available."
Mr Daly added LED or electric candles should be used, especially in the festive season when clothing and decorations can pose additional hazards.
London Ambulance Service attended the scene on Wednesday afternoon and later called officers from the Metropolitan Police, who are not investigating the incident.
The Health and Safety Executive was also informed.
Croydon Council will now review the incident with the school, the Archdiocese of Southwark and London Fire Brigade.
A council spokesman said: "Our thoughts are with all those affected by this very sad incident and we are supporting staff, pupils and the wider school community.
"We will be working closely with the school, the diocese and London Fire Brigade to review the circumstances to minimise the risk of anything like this happening in the future."
Head teacher Noel Campbell said: "Our whole school community is devastated by the incident that occurred at our carol service yesterday.
"Our thoughts and prayers are with the child and his family at this difficult time.
"Following this incident, our pupils, staff and families are being given support."
A statement from the archdiocese said: "The Archdiocese of Southwark was informed of an incident that occurred at Our Lady of the Annunciation Catholic Church in Addiscombe, which led to a child suffering serious burns and two adults also sustaining injuries.
"At this time our thoughts and prayers are with the child and those injured, their families, and the school and parish community.
"The archdiocese and school involved are co-operating fully with the ongoing investigation."
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