The attack on Thursday came two days after campaigning began for next month's presidential election in the war-ravaged country.
"There were four impacts downtown and a fifth impact near Camp Warehouse," International Security Assistance Force (ISAF) spokesman Lieutenant Commander Ken Mackillop said.
A woman and a child were injured in the attack, Kabul police chief General Babajan said.
The four rockets were all fired at the same district, he added. One of the rockets fell in a garden next to a mud-brick house.
"One woman has been injured in my neighbour's house, she has been taken to the hospital," said Abdul Wakeel, a local resident.
Other neighbours said an 11-year-old boy was also injured.
Deputy police chief Mutahullah Khan Rahmani said two rockets were fired from north-eastern Kabul and fell on the houses of an Afghan colonel and a police officer but neither exploded.
Remnants of the Taliban – driven out of power by the US-led forces in December 2001 - have vowed to disrupt Afghanistan's 9 October polls.
In less than two months there have been five rocket strikes on Kabul, not including Thursday's, compared with a total of around 20 since 2002.
On 29 August, a car bomb blast hit a US security firm in the capital, killing between seven and nine people.