The salvo slammed into various parts of central and north Kabul — including near the heavily fortified Green Zone that houses embassies and international companies — just before 9:00 am (0430 GMT).
“This morning, the terrorists fired 14 rockets on the city of Kabul,” interior ministry spokesman Tariq Arian said.
“Unfortunately the rockets hit residential areas. Until now, three of our countrymen were martyred and 11 others were wounded.”
Kabul police spokesman Ferdaws Faramarz confirmed the same death toll and details, while health ministry spokeswoman Masooma Jafari put the toll at five dead, 21 wounded.
Photos and videos circulating online showed several buildings with damage to walls and windows, including at a large a medical complex.
No group immediately claimed the blasts and the Taliban denied responsibility.