The provincial security commandment in a statement said the incident took place at around 12:30 pm local time in Ghazni city.
The statement further added that five Taliban militants including their commander were attempting to move a vehicle packed with explosives to an unknown location in Ghazni city when the incident took place.
Provincial Security Chief Gen. Farid Ahmad confirmed that the incident took place in the vicinity of the 3rd police district of the city and a number of the houses have also been damaged.
In the meantime, the provincial security commandment said the Taliban commander killed in the explosion has been identified as Rahimullah, also famous as Mullah Zakir.
The anti-government armed militants including Taliban insurgents have not commented regarding the incident so far.
Ghazni is among the relatively volatile provinces in southeastern parts of the country where the Taliban militants and terrorist belonging to the other groups are actively operating in some of its districts.