Abdul Wasay Rahimi, Deputy Police Chief of Parwan said the missiles were fired at around 9 p.m. last night.
In retaliation, the U.S. airstrikes have hit Dasht-e Qalandar Khail village of Bagram district, the official added.
He did not comment regarding the possible casualties.
The Taliban insurgent group has claimed responsibility for the attack.
Meanwhile, a key Taliban member has been arrested by police in the province.
Provincial police spokesman Salim Noori said on Thursday that a key Taliban member identified as Hameedullah was arrested in Shinwar district of the province.
He further said that the detained individual was involved in destructive activities in Ghorband district of the province.