School security guards and staff managed to restrain the 39-year-old attacker.
The woman, identified only by her surname Liu, has been arrested, Hong Kong-based South China Morning Post quoted a local state-run Chongqing Broadcasting Group as saying.
Police are now investigating and no motive has been given for the attack.
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The attack at the Xinshiji Kindergarten in the outskirts of Chongqing occurred around 9.30 am local time, when the children were returning to their classes.
All victims have been hospitalized and receiving treatment, according to police.
In another incident past year, a man climbed the wall of a kindergarten and knifed 11 children.
The incident happened soon after a Chinese court awarded the death sentence to a man who killed nine children in a school attack in Shaanxi province last April.
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The use of knives for crime is common, because there is much strictness on gun controls in China.
Nearly 20 children were killed in school attacks in 2010, prompting a response from top government officials and leading many schools to add gates and security guards.
A vehicle crashed into a large crowd of people in Hengdong County, central China's Hunan Province on Wednesday evening, killing 11 and injuring a further 44.
In June, a man used a kitchen knife to attack three boys and a mother near a school in Shanghai, killing two of the children.
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