An Afghan local police commander told Al Jazeera that 10 police officers were killed in the attack which started at about 4am on Saturday.
The toll differed slightly from that given by the parliamentary representative for the province, Abdul Wali Niazi, who told local media that seven police had been killed and three had been taken hostage.
Abdullah Naji Nazari, the head of the provincial council, did not confirm the casualty figures, but said the centre of Yamgan had been captured by the Taliban.
"The situation is tense and worrying if reinforcements are not sent in time," he said.
Taliban spokesman Zabiullah Mujahid said fighters had taken control of several checkpoints and the district centre, killing several members of Afghan forces and seizing weapons.
Al Jazeera's Nicole Johnston, reporting from Bamiyan, in central Afghanistan, said security forces were regrouping and planning an offensive to retake the district.
Johnston said the country's north has become a new fighting front for the Taliban over the past two months, during its annual Spring offensive.
"That area in the north is more exposed. There are not as many security forces up there," she said.
In early May, at least 18 Afghan policemen were killed in a series of Taliban attacks in Badakhshan province.
A surge in attacks has taken a heavy toll on civilians, according to the UN Assistance Mission to Afghanistan.