State broadcaster CCTV said the driver "lost control" of the vehicle as it approached the school in Shandong province's Tai'an city at 7:27 am (2327 GMT Monday).
The bus ran into a group of parents and children on the side of the road, according to CCTV.
"As of now, (the incident) has caused the deaths of 11 people, of whom six were parents and five were students," the broadcaster reported in an update just after 11:30 am.
It said one other person was in a "critical" condition, while the vital signs of another 12 people were "stable".
Photos and videos circulating on social media showed people in blood-soaked clothes lying in the road near a hulking grey bus.
Several adults knelt over children sprawled unmoving on the ground, while other people could be heard screaming in the background.
"They're all dead, it's so heartbreaking," a woman's voice could be heard saying off-camera in one clip of the aftermath of the crash.
"I'd have been killed too if I'd stood there, but luckily I ran away fast," she said.
AFP was able to geolocate several of the social media photos and videos to the school in Shandong where the crash took place.
The driver was being held by local police and the cause of the incident was "under investigation", CCTV said.
Many public schools in China reopened for the new academic year this week.
Deadly traffic accidents occur frequently in the country due to lax safety standards and widespread disorderly driving.
In July, police said a vehicle crashed into pedestrians in the central city of Changsha, killing eight people and injuring five.
A 55-year-old suspect living in the area was detained pending an investigation, but it was not clear if the incident was intentional or not.
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