The South Eastern Education and Library Board bus and a van collided on the Vianstown Road in Downpatrick on Tuesday morning.
Thirteen children who attend Knockevin Special School were on board the bus, along with two adults.
A PSNI spokesperson said the special needs pupils were not hurt but were "extremely shaken" by the crash.
The children were helped out of the bus by passersby, who brought them to a nearby house where they waited until the emergency services arrived.
They were then taken to the Ulster Hospital in Dundonald and Downe Hospital in Downpatrick.
One teenage boy was kept in for further investigations at the Ulster, while all others were discharged.
Darrell McCoubrey's six-year-old brother-in-law was one of the pupils caught up in the crash. He said it was a frightening experience, but he is now "running about as usual".
Mr McCoubrey praised the actions of those who helped at the scene of the crash.
"Everybody that pulled up on the scene... car doors lying open, running up... there was no hesitation everyone was straight up to the scene to see what they could do to help," he told UTV.
Given the nature of the accident, the rolling over of the bus, I've no doubt that the seat belts helped prevent serious injury on this occasion.
Dr Nigel Ruddell
Dr Nigel Ruddell from the NI Ambulance Service said the emergency services declared the crash to be a major incident.
"I'm pleased to say that on first appearances none of the children seemed to have any life threatening or serious injuries.
"I think that's testament to the fact that all these children were wearing seat belts in this school minibus otherwise it could have been very different," he explained.
Education Minister John O'Dowd said: "All pupils, their escort, the bus driver and the driver of the other vehicle have been taken to hospital and my thoughts are with them and their families following this distressing incident.
"I know the emergency services were promptly on the scene and I would like to thank them for their work this morning."
Sinn Féin MLA Chris Hazzard has praised the bus driver for making sure the children were brought to safety.
"Although shocked himself I believe the driver worked to make sure that the children were comforted.
"I am relieved that no one was seriously injured and hope that everyone makes a full and speedy recovery," he said.
SDLP MLA Seán Rogers said his thoughts are with the passengers and their families.
"This must have been a very traumatic ordeal for them all. Initial reports state that all of the passengers were strapped into their seats. This clearly re-emphasises how vital such seat belts are," he added.
"I wish all concerned a full speedy recovery."
The Vianstown Road was closed and diversions put in place at its junction with Bonecastle and Ballydugan Road.