In an operation in the southern Helmand province, long a hotbed of insurgent activity, Hafiz Wahidi and nine of his men were killed, the ministry said in a statement.
Wahidi is the second militant commander who claimed links to the extremist IS group, to be killed in Helmand. His uncle, Adbul Rauf Khadim, was killed in a drone strike in February.
Khadim was a former Taliban commander who had switched allegiance and aligned his followers with the Islamic State group, which controls about a third of Iraq and Syria in a self-declared caliphate. He had allegedly set up an IS recruiting network across southern Afghanistan.
President Ashraf Ghani has mentioned the threat posed by the group in recent speeches and is due to visit Washington next week where he is expected to request an extension of the American military presence as his government battles the Taliban, al-Qaida and possibly IS on a number of fronts.
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Today's operation in Helmand appears to have been part of a major military offensive against the Taliban and other insurgent groups ahead of the warm-weather fighting season.
After being cleared from a number of its strongholds in the past two months, the Taliban has launched a ferocious backlash with suicide bombings and attacks on police and civilians.