Police said they have arrested a 25-year-old man with the surname Wu in Lianjiang town.
The other victims are a teacher and two parents, AFP reported, quoting a local city official. One person is also injured.
The attack happened on Monday at 7.40am local time.
The man was arrested at 8am and police have called this a case of "intentional assault".
A storeowner who works near the kindergarten told the BBC the surrounding area has been sealed off.
The attack has sparked widespread conversation across Chinese social media platforms, with many users responding in shock.
Violent crime is relatively rare in China, but the country has seen a spate of knife attacks in recent years, including several in schools.
In August last year, a knife-wielding assailant stormed a kindergarten in the south-eastern Jiangxi province, killing three people and wounding six others.
In April 2021, two children died while 16 others were injured during a mass stabbing in Beiliu City, in Guangxi Zhuang autonomous region.
In October 2018, 14 children were injured in a knife attack at a kindergarten in Chongqing, south-west China.
Chinese authorities have been stepping up security around schools since 2010.
That year, the Ministry of Public Security had urged local authorities to "resolutely crack down" on criminal activities to ensure the safety of teachers and students.
After the April 2021 attack, the education ministry also mandated emergency evacuation drills in schools.