The girl's father complained to police in Shanxi province in northern China in mid-October that his daughter was hit hard enough to leave bruises and swollen eyes, Xinhua, the official government news agency, reported.
Investigators released video from a security camera that showed the teacher striking the child over and over in a 10-minute period.
The Sky Montessori kindergarten in the provincial capital, Taiyuan, had 43 pupils when its closing was ordered, officials said.
Police said the teacher, identified as Li Zhuqing, hit the girl because she had trouble with arithmetic. Officials said the teacher is now serving a 15-day detention order.
Officials in Taiyuan said all kindergartens in the city are being inspected and those found wanting will be closed.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'