It was not clear how old the injured children are, 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 attack took place in the Henan province village of Chengping just before 8am, said a police officer from Guangshan county, where the village is located.
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 ill 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.