The militants initially detonated explosives near the entrance gate of the ministry compound to allow the remaining insurgents to intrude inside the ministry.
The attack sparked heavy clashes that lasted for almost two hours before the assailants were shot dead by the security forces.
The Ministry of Interior spokesman Najib Danish said the attack was carried out by a group of at least ten insurgents and all of them have been killed during the clashes with the security forces.
The officials did not disclose further information regarding the casualties inflicted on the security forces and the civilians during the attack.
Danish had earlier said that one guard of the ministry was wounded in the first blast near the entrance gate.
However, another security source has said that the attack has left at least nine people dead or wounded.
No individual or group has so far claimed responsibility behind the attack so far.
But the Taliban group had earlier warned that they will carry out attacks on security institutions in the capital as part of their spring offensive.