The local authorities said a number of women and children are also among those killed or wounded.
The provincial government media office in a statement said the incident took place in the vicinity of Surkh Rod district at around 7 am local time.
The statement further added that a woman was killed along with her daughter and another child in the explosion and at least eight others were wounded.
According to the local authorities, at least eight other children including two girls sustained injuries in the explosion.
The officials are saying that the Taliban militants fired a rocket late on Saturday night which landed in Surkh Rod district but did not go off.
The explosion earlier today took place while the children were playing in the area, the officials said, adding that the injured civilians have been shifted to the provincial hospital for the treatment.
The statement by the provincial government also added that the health condition of two of the children has been reported as critical.
The anti-government armed militant groups including Taliban insurgents have not commented regarding the report so far.