General Mohammad Zahir, director of the criminal investigation division of the Kabul police, said the rockets landed in north eastern Kabul near a private television station and close to an office compound used by the Afghan intelligence service.
Daud Amin, deputy police chief of Kabul, said a total of four rockets were fired on the city, damaging one home.
Insurgents occasionally launch rockets into the city, but the weapons are not very accurate and frequently miss their targets.
These latest rockets were launched from the east and north eastern parts of the city, but did not penetrate the centre of the capital.
Dr Sayed Kabir Amiry, director of all the Afghan hospitals in Kabul, said a 28-year-old man was killed in one of the rocket attacks and three other people were wounded.
One person who was wounded had been discharged from the hospital, but the other two were still being treated, he said.