The provincial government media office in a statement said the incident took place on Wednesday in the vicinity of Khogyani district.
The statement further added that an Improvised Explosive Device planted by the Taliban insurgents went off Aabko area, leaving the 4-year-old child dead.
The anti-government armed militant groups including the Taliban militants have not commented regarding the report so far.
The anti-government armed militant groups frequently use explosives materials for the roadside bombings and car bombings to target the government staff and security personnel.
However, in majority of such incidents the ordinary civilians are targeted besides such bombings incur casualties to the security personnel and in some cases the Taliban militants themselves are killed or wounded.
Earlier, at least three militants affiliated with the Islamic State of Iraq and Syria (ISIS) terrorist group were blown up by own explosives in eastern Nangarhar province of Afghanistan.
The local security officials said the incident took place late on Sunday in the vicinity of the restive Achin district.
The officials further added that the militants were looking to plant an Improvised Explosive Device in Ghani Khel area when the incident took place, leaving three of them dead.