The Year 9 pupils were in a sports hall at Minster College, in Minster Road on the Isle of Sheppey, Kent, when the accident happened.
Emergency services were called to the scene shortly after 9am.
Six teenagers were taken by ambulance to Medway Hospital, four of them with neck, head or back injuries.
The school was closed for the day and headteacher Alan Klee said arrangements were being made for pupils to be collected.
A spokesman for South East Coast Ambulance Service said: "We were called today at 9.14am to initial reports of a roof collapse at Minster College, Minster Road, Sheerness.
"We sent 11 vehicles to the scene. They included emergency ambulances, single responder cars and patient transport ambulances.
"There are currently 13 confirmed casualties, all of whom are teenagers.
"Four of the patients have serious neck, head and/or back injuries.
"The other nine have more minor injuries.
"A small number of people also received treatment at the scene for things like shock.
"Six patients have been taken to Medway Hospital by land ambulance.
"The air ambulance was called to the scene but no patients were airlifted.
"Some paramedics are still at the scene."
A Kent Police spokesman said: "It's been confirmed that 13 Year 9 pupils have been injured.
"They were sitting an exam in the sports hall when the incident occurred."
Kent Fire and Rescue Service said no-one was believed to be trapped following the collapse.
Mr Klee said: "During an exam being sat by Year 9 pupils in the sports hall at Minster College, heating ducting collapsed.
"Twelve first aid-trained staff dealt with injuries immediately and emergency services were on site within a few minutes. The school is currently co-ordinating the collection of all the children. Any children who can't be collected will remain on site fully supervised.
"For further information please call the Kent County Council contact centre on 08458 247 247."
Mr Klee said that the heating duct had largely fallen between the desks so had missed most of the 150 students who were sitting in the hall.
Speaking to reporters outside the school which has been closed for the day, he said: "We were very lucky indeed. Most of the students have escaped with just cuts and bruises and are being discharged from the hospital as I speak. It's very fortunate that it fell between the desks so it missed many of the students.
A spokesman from Medway NHS Foundation Trust in Gillingham said: "Medway NHS Foundation Trust has admitted 11 patients who sustained injuries at Minster College.
"At the moment there are no obvious serious injuries but investigations are ongoing. There are a number of head and neck conditions being assessed and families are here at the hospital. "
The hospital spokesman said later: "This morning's emergency was officially stood down at 1.30pm. "We are still dealing with a number of patients but currently no serious injuries have been identified. The accident and emergency department will be accepting all 'blue light' emergencies from 1.45pm."
Pupil Sam Millen, 13, was in the sports hall when the heating duct fell.
He said: "We'd been doing our exam for about 20 minutes when there was a loud creak in the air vent, which was attached to the ceiling in a U-shape.
"We heard a bit more creaking and then the whole back bit fell down. There was no one at the back of the hall but then it started coming down at the side as well and hitting people, but not very badly.
"It looked like one boy at the front was crushed under a piece of metal and everyone started panicking and screaming."
Sam said the whole structure came down in about "five to 10 seconds".
He said that pupils, who were sitting an exam in Preparation for Working Life, were told to leave the room by invigilators who were overseeing the test.
"It was extremely frightening," he added. "It all happened so quickly, no one knew what was going on."
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