According to the broadcaster, which cited provincial officials, the explosion took place in the commander's house in the province's southern Garmsir district on Sunday as he was making the device.
Two members of the Taliban commander's family were among those killed by the explosion, while the injured included four children and seven women, the news outlet added.
Afghanistan has long been suffering from an unstable security situation. The government has been fighting against Taliban, which has been waging a war against Kabul for almost two decades, and Daesh*, which has been operating in Afghanistan since 2015.
Another deadly attack, claimed by Daesh, was launched in a mosque in the eastern city of Gardez just two days prior, killing at least 30 people and injuring 81.
*Taliban, Daesh [the Islamic State, ISIL, IS] — terrorist groups banned in Russia