A specialist Urban Search and Rescue team and equipment were also used to confirm the building was at no further risk of collapse
The fire brigade was called to Rosemead Preparatory School and Nursery on Thurlow Park Road in Dulwich at 9.22am Monday morning.
The building was evacuated and 16 people were treated on the scene for minor injuries while 13 people were taken to hospital by London Ambulance crews, London Fire Brigade said.
None of the injuries were life threatening.
A London Ambulance Service spokeswoman said: “We were called at 9.24am today to reports of an incident at Rosemead Preparatory School.
“We sent a number of resources to the scene, including ambulance crews, medics in cars, advanced paramedics, incident response officers, emergency planning resilience officers, our hazardous area response team, and a command support vehicle.”
They added: “We treated 16 people at the scene, and took 12 children and one adult to hospital.”
Firefighters carried out a systematic search of the building and confirmed with the school that all children and staff were accounted for, the fire brigade said.
Three fire engines and around 20 firefighters from West Norwood and Brixton fire stations attended the incident, which was over by 11.50am.
A specialist USAR (Urban Search and Rescue) team and equipment were also used to confirm the building was at no further risk of collapse.
All children have been accounted for and the school, a fee-paying prep school for children aged two-and-a-half to 11, is in the process of contacting parents, the Metropolitan Police said in a statement.
A spokesman for the Metropolitan Police said: “London Fire Brigade called police at approximately 09:25hrs on Monday, 15 November following reports of a ceiling collapsed at a school on Thurlow Park Road, SE21.
“Officers are in attendance at the school alongside London Fire Brigade and London Ambulance service.
“All children and staff have been accounted for and the school is currently in the process of contacting parents.
“We await an update on assessment of any injuries.
“There are extensive road closures in place as emergency services respond.”
Helen Hayes, the Labour MP for Dulwich and West Norwood thanked the fire brigade for their response and offered her support to the school.
Writing on Twitter, Ms Hayes said: “Very concerned to hear of the collapse of a ceiling at Rosemead School this morning.
“My thoughts are with the children, staff and parents. I hope no one is seriously injured.
“I’ve contacted the school to offer my support.
“My thanks to the emergency services who attended the scene.”
A statement from Rosemead Preparatory School said: “This morning in one of our Year 3 classrooms, a ceiling collapsed resulting in the attendance of the emergency services.
“Some injuries were sustained and some of those involved have been taken to hospital, and we are working with our students and families to support them.
“We are working closely with the authorities to understand the cause of the incident and we will provide more information as soon as we can.
“Parents and families can be reassured that the school day is continuing as usual today for the rest of the school.”
Nick Crawford, the chair of governors of Rosemead Preparatory School confirmed there were no concerns regarding the rest of the building.
He said: “We understand from initial examinations that there are no concerns regarding the rest of the building and we will work with the authorities regards any investigations to be undertaken.
“I would sincerely like to thank members of staff, the emergency services and those who sent messages of support from the wider community.”
Additional reporting by PA