"This morning, 10 rockets were fired from the Labe Jar neighbourhood of Kabul," ministry spokesman Tariq Arian told reporters.
He said three rockets landed near Kabul airport and seven in residential areas, leaving one civilian dead and two wounded.
No group has claimed the attack so far and the Taliban denied any involvement.
Kabul police confirmed the early morning attack.
The barrage of rockets on Saturday was the second such attack in less than a month in Kabul.
On November 21, eight people were killed when 23 rockets hit the capital in an attack.