Local highway police commander Sahib Jan said at least one more police officer was wounded in the attack in the village of Rabat, Press TV reported.
The attack came after U.S.-led forces claimed to have killed 10 militants, including a top militant leader, in the province, the Iranian network said.
Meanwhile, two roadside bombs went off near Afghan and international convoys in Wardak province Monday but an official said there were no injuries.
Provincial spokesman Adam Khan Sirat said both attacks occurred in Sayd Abad district, Xinhua reported.
"The first roadside bomb went off at noontime targeting a convoy of the Afghan national army, while the second one detonated by remote control hit a convoy of international troops, fortunately no causalities on both forces." Sirat told Xinhua.
Zabihullah Mujahid, a purported Taliban spokesman, told the state-run Chinese news service the insurgents destroyed two military vehicles.
Four Canadian soldiers were killed and eight more wounded by two roadside bombs in Afghanistan last Friday, just days before they were to have been rotated back home, military officials say.