The women had gathered outside a high school in eastern Kabul demanding the right for girls to return to secondary school.
The war in Afghanistan has ended, but the conflict on who represents the people of that war-torn country remains unresolved.
Pemimpin Tertinggi Taliban Hibatullah Akhunzada berkata kerajaan baru akan bekerja keras untuk patuh kepada peraturan Islam dan undang-undang Syariah.
Smoke could be seen rising above buildings in the north, where the Hamid Karzai International Airport is located.
Local media reported possible civilian casualties, which the US says it is assessing.
The pair are among six being interrogated by the Taliban.
Scores died in the Islamic State-claimed attacks, including 13 US servicemen.