The Ministry of Interior (MoI) says the three attackers who started resistance with the security forces after the explosion were shot dead after almost four hours of gun battle.
MoI further added that only one policeman sustained injuries in the attack and the embassy staff were evacuated safely by the security personnel.
Earlier reports had emerged that a security guard of the embassy was killed and some others were wounded in the attack.
The Emergency Hospital in the meantime says at least two people wounded in the attack were shifted to the hospital for the treatment.
The Islamic State of Iraq and Syria (ISIS) terrorist group also known as Daesh has claimed the responsibility behind the attack on the embassy of Iraq in Kabul city.
The group has issued a statement both in Dari and Arabic language claiming that the attack was carried out by two suicide bombers.
This was the second attack carried out by the anti-government armed militant groups in the past one week which followed the deadly car bombing that left at least 24 dead and 42 others wounded last week.