This comes despite President Ashraf Ghani's call for a ceasefire with the Taliban during the Muslim holiday of Eid al-Adha.
Mr. Ghani's announcement, during a televised speech marking Afghanistan's independence day, came on the heels of an unusually deadly wave of violence across the country, most of it carried out by the Taliban, that has left at least 325 soldiers, police and civilians dead in the past 10 days.
He said his forces had not kidnapped the passengers but had taken them to a safe place near the highway to question them and will free them after the investigations are finished.
He said the "last ceasefire in Afghanistan revealed the deep desire of the Afghan people to end the conflict, and we hope another ceasefire will move the country closer to sustainable security".
The fate of the hostages in Kunduz province - in an area that has recently fallen under Taliban control - was not immediately known and there was no statement from the insurgents.
The buses, carrying passengers from Badakhshan and Takhar provinces, were on their way to the capital, Kabul, according to Abdul Rahman Aqtash, police chief of the Takhar province. The Taliban accepted that three-day ceasefire, but later rejected a call by the president to extend it.
Trump cancels military parade, blaming costs on Washington officials - Ireland
But after months of planning, the Pentagon said Thursday that the president-proposed event has been postponed until at least 2019. The Defense Department says the Veterans Day military parade ordered up by President Donald Trump won't happen in 2018.
Kunduz provincial council member Sayed Assadullah Sadat said people on the buses were travelling to be with family in Kabul for the holiday.
They have warned they will be releasing 500 prisoners, including some Afghan security forces.
In a statement issued by US Secretary of State Michael Pompei he said: "This plan responds to the clear and continued call of the Afghan people for peace".
The June ceasefire - the first such truce in the country since the 2001 United States invasion - spurred hopes that a new path was opening for possible peace talks in the country to the end the almost 17-year-old war.
"It is our hope, and that of the worldwide community, that the Afghan people may celebrate Eid al-Adha this year in peace, free from fear", he added, referring to the Islamic holiday that starts next week. The heavy casualties underscore the challenges the government in Kabul faces since the USA and North Atlantic Treaty Organisation officially ended their combat mission at the end of 2014.