There were conflicting reports of casualties during the initial hours of the explosion.
Later on, the Ministry of Interior in a statement said that up to 10 people were killed and five others including Kunduz police chief were injured in the attack.
According to the statement, Kunduz police chief was briefing journalists when the suicide bomber detonated his explosives.
Sayed Sarwar Hussaini, the provincial police spokesman, a journalist, and several other police members are said to be among the deads.
The Taliban insurgent group that attacked the Kunduz city from several directions early this morning, claimed responsibility for the attack.