The attack in the Henan province village of Chengping happened shortly before 8 a.m., said a police officer from Guangshan county, where the village is located.
The attacker, 36-year-old villager Min Yingjun, is now in police custody, said the officer, who declined to give her name, as is customary among Chinese civil servants.
A Guangshan county hospital administrator said the man first attacked an elderly woman, then students, before being subdued by security guards who have been posted across China following a spate of school attacks in recent years. He said there were no deaths among the nine students admitted, although two badly injured children had been transferred to better-equipped hospitals outside the county.
A doctor at Guangshan's hospital of traditional Chinese medicine said that seven students had been admitted, but that none were seriously injured.
Neither the hospital administrator nor the doctor would give his name.
It was not clear how old the injured children were, but Chinese primary school pupils are generally 6-11 years old.
A notice posted on the Guangshan county government's website confirmed the number of injured and said an emergency response team had been set up to investigate the attacks.
No motive was given for the stabbings, which echo a string of similar assaults against schoolchildren in 2010 that killed nearly 20 and wounded more than 50. The most recent such attack took place in August, when a knife-wielding man broke into a middle school in the southern city of Nanchang and stabbed two students before fleeing.
Most of the attackers have been mentally disturbed men involved in personal disputes or unable to adjust to the rapid pace of social change in China, underscoring grave weaknesses in the antiquated Chinese medical system's ability to diagnose and treat psychiatric illness.
In one of the worst incidents, a man described as an unemployed, middle-aged doctor killed eight children with a knife in March 2010 to vent his anger over a thwarted romantic relationship.