The attacks occurred on pedestrians in the morning in Gongyi city in central Henan Province, the state-run Xinhua news agency reported.
Police said one child and three of the adults died at the scene, while the other child and one adult died in a hospital despite emergency treatment, a city official said.
The children were 1- and 4 years old. The dead adults included one man and three women.
Witnesses said the man appeared to be attacking pedestrians at random.
Cao Jianli, a civil servant, said the attacker, reported to be a 30-year-old local farmer, dropped his ax after being surrounded by police, Xinhua reported.
"I and several of my colleagues rushed out to the street when we heard people crying for help. We used mops to fend off the ax-wielding man and waited for the police to come," Cao said.
Police, who are investigating the killings, said the assailant's medical records indicate he suffers from schizophrenia.