Provincial security chief, Fazaluddin Ayar said the operation was launched early Friday morning in Yamgan district.
Ayar further added that the operation was jointly launched by Afghan police, Afghan army and Special Forces.
He said Afghan national army soldiers and the Special Forces have managed to enter Yamgan district and operation is still being carried out to clear the area from militants.
According to Ayar, at least six policemen were injured during clashes with the Taliban militants.
Dozens of Taliban militants attacked Yamgan district earlier this week and managed to take control of the district following hours of gun battle.
At least 27 policemen were also abducted by Taliban militants following the attack, local official said.
Badakhshan is among the relatively volatile provinces in northeastern Afghanistan where anti-government armed militant groups have increased their activities recently.