"Many schoolchildren were injured, the specific casualties are being investigated," state broadcaster CCTV said.
State media did not say if the crash was deliberate.
Video circulating on Chinese social media that matched images of the school online appeared to show the aftermath of the incident, with dozens of children running in panic away from the site of the crash.
Several people, including a young child, can be seen lying on the ground.
Another showed a bloodied man being beaten with sticks by passersby as he lay on the ground next to an SUV.
The crash took place outside Yong'an primary school in the central Chinese city of Changde.
China has seen several mass casualty incidents in the past week, sparking extensive discussion online about the rising number of seemingly random acts of violence against civilians.
Last Monday, a man killed 35 people and wounded more than 40 more when he rammed his car into a crowd in the southern city of Zhuhai -- the country's deadliest attack in a decade.
But authorities took almost 24 hours to release that toll, and videos of the attack later appeared to be scrubbed from social media.
Police said the suspect, surnamed Fan, had been "triggered by... dissatisfaction with the division of property following his divorce".
And on Saturday, eight people were killed and 17 others wounded in a knife attack at a vocational school in eastern China.
Police said the suspect was a 21-year-old former student at the school, who was meant to graduate this year, but had failed his exams.
Beyond the incidents in Yixing and Zhuhai, there has been a spate of other attacks.
In October, in Shanghai, a man killed three people and wounded 15 others in a knife attack at a supermarket.