General Abdul Rahman Sayed Kheil, a provincial police chief, said the bomber entered the police station while Afghan officials were meeting US soldiers advising a police training programme.
He said the blast killed an American soldier and wounded two others. Four Afghan security officers were also wounded in the blast.
Zabiullah Mujahid, a Taliban spokesman, claimed responsibility for the blast in a phone call to the Associated Press, the news agency reported.
The attack which took place in Pul-e-Khumri, the provincial capital of Afghanistan's Baghlan region.
The US military said it was aware of an incident including some casualties but could provide no further details.