According to the ministry two rockets landed near Hamid Karzai International airport but no casualties were reported. Another two rockets landed in Khwaja Rawash residential area killing one person and wounding another.
However residents in the Khair Khana area said nine rockets were fired off. Video footage on social media also clearly shows at least eight rockets being fired off.
No group has yet claimed responsibility.
This is the second rocket attack in the city in less than a month.
On November 21, about two dozen mortar shells hit downtown Kabul killing at least eight people and injuring 31 others.
The rockets that were fired from the back of two vehicles slammed into different parts of the capital.
ISIS (Daesh) claimed claimed responsibility for the attack,