Saber Khan was killed as he was on his way to inspect police checkpoints, said Shapoor Ahmadzai, a spokesman for provincial police.
Two of his guards were wounded in the bombing which happened around 8:00a.m., the official said.
Abdul Wali Wakil, a provincial council member, however said the bombing killed also two guards and wounded another two.
Taliban spokesman Zabihullah Mujahid said that the attack was carried out by the group.
Separately, Defense Ministry in a statement said that 45 militants were killed in army operations over the past 24 hours.
The operations were carried out in Laghman, Logar, Uruzgan, Badghis, Balkh, Baghlan, Kunduz and Helmand, the statement said. Eight insurgents were arrested, it added.