The attack by 250 to 300 insurgents continued for over a day in Badakhstan province's remote Yamgam district, said Asadullah, the police chief of adjacent Jurm district.
"The police force...ran out of ammunition and food, and that is how the Taliban took 27 of them as captives," he said.
"The district headquarters has fallen to the Taliban after they launched an attack. We could not send reinforcements," said Seiq Seddiqi, a spokesman for Afghanistan's Interior Ministry.
Overrunning a remote police outpost is a common Taliban maneuver. In February, 21 Afghan soldiers were killed in Konar province, and 18 police officers were killed in Badakhshan in September 2013, under similar circumstances.
The attack at Yamgam highlights the vulnerable nature of Afghan units across the country. The presence of Afghan military and police units in remote areas now lacks air support from United States troops, and Afghan officials have made units in remote locations a priority.