The attacker also injured 13 others on the bus, Xinhua News Agency reported. The incident occurred Monday in Anyang.
Those killed included an 18-year-old youth, a 10-year-old boy and the 10 month-old girl, the report said.
Police said the attacker had planned to rob the passengers.
The report said there were 33 passengers on the bus and 15 of them were injured.
Other details were not available and it was not clear how the attacker managed to attack so many people with a knife and still manage to escape after forcing the bus driver to stop the vehicle near a corn field.
Anyang police posted a reward of $16,000 for information leading to the capture of the assailant.