Other rockets landed near the international airport, the city centre and in the eastern part of the city, where several NATO military camps are located.
Footage on Tolo, a private television channel, showed several houses and a car with their windows blown out in downturn Kabul.
The rockets were fired from from Deh Sabz, on the northeastern outskirts of Kabul.
Taliban claimed responsibility for the attack in a statement posted at their website, saying the targets were army bases and the international airport.
Tuesday's attacks were the biggest in Kabul in several years.
The attacks in the Afghan capital came ahead of the Aug 20 presidential election after the government had said Kabul would be the safest locale for the voting in the country plagued by a Taliban-led insurgency.
The Taliban is boycotting the polls and has ordered all its fighters through a statement posted on its website last week to disrupt the election and intensify assaults on Afghan and international military targets.
'We expected that the enemies attack before the elections and they are doing this to dismantle the process, but we will never let them do that, we will never let the enemies fulfill their negative targets and aims,' Bashary said.
'This was a disturbing attack and we will investigate it,' he added.