The stampede took place at the Experimental Primary School of Puyang County when students were returning after a toilet break to take a test.
Twenty others who had been injured were sent to hospital, with five of them in critical condition.
The principal and vice principal of the school have been suspended for investigation, the county's head of education bureau told state-run Xinhua news agency.
"The students were going to have a test after the break, so many went to the toilet. Some students on the second floor fell down on the staircase causing others to lose balance and tumble down," Liu Wenhua, the school's vice principal who witnessed the accident, was quoted as saying.
The local government has set up a team to investigate the incident.