According to the statement, a group of Taliban militants attacked police checkpoints in Panah village of Giro district on Monday morning.
Taliban key commander along with four of his bodyguards have been killed, the statement added.
MoI said, six other Taliban militants have also been injured during the attack on Monday.
Taliban have not commented regarding the report so far.
Ghazni is among insecure provinces in eastern Afghanistan, where armed militants are actively operating.