Three gunmen held siege the Barchi National Hospital in Kabul for hours after the early-morning attack before security forces killed them in a clearance operation, the interior ministry said.
Heavily armed security forces were seen carrying infants away from the scene - at least one wrapped in a blood-soaked blanket.
"The fatalities also include mothers and nurses," interior ministry spokesman Tareq Arian said.
Some 15 people were wounded and more than 100 - including three foreign nationals - were rescued, he said.
The hospital is located in the west of the city, home to the capital's minority Shia Hazara community - a frequent target of hardline Sunni militants from the Islamic State group.
A paediatrician who fled the hospital told AFP he heard a loud explosion at the entrance of the building.
"The hospital was full of patients and doctors, there was total panic inside," he said, asking not to be named.
The hospital is supported by the humanitarian organisation Doctors Without Borders (MSF), and a number of foreigners were working at the hospital.
Tuesday's attack was the latest hitting the country's already stretched health sector, with facilities and medical personnel frequently caught in the crossfire during decades of war in the country.
"We call on all sides to stop attacking hospitals and health workers," said deputy health minister in the city, Waheed Majroh.
Around an hour after the Kabul assault, a suicide bomber killed at least 24 people at the funeral of a local police commander in eastern Nangarhar province, according to provincial spokesman Ataullah Khogyani.
The attacker detonated explosives in the middle of the ceremony.
Amir Mohammad, who was wounded in the blast, said thousands of people had gathered for the funeral, an event that often draws huge crowds in Afghanistan.
The Taliban denied involvement in either attack.
The violence comes just a day after four roadside bombs exploded in a northern district of Kabul, wounding four civilians including a child.
Those bombings were later claimed by the Islamic State group, according to the SITE intelligence group.
They were just the latest in a string of IS attacks on the capital.
In March at least 25 people were killed by a gunman at a Sikh temple in Kabul in an attack later claimed by the group.
IS was also responsible for an infamous attack in March 2017 on one of the country's largest hospitals, when gunmen disguised as doctors stormed the Kabul building and killed dozens.