The Afghan interior ministry said at least eight people were killed in the attack on the Dasht-e-Barchi Hospital and several more were injured.
The 100-bed government-run facility is supported by Doctors Without Borders, which is also known by its French name Médecins Sans Frontières (MSF), said Wahidullah Mayar, a spokesman for the Ministry of Public Health.
There was no immediate claim of responsibility, but the Taliban said they were not involved.
Security forces were working to counter the attack, an interior ministry source said. He added that the deputy health minister may have been visiting the clinic at the time of the attack.
Two other security sources said explosions had been heard at the site.
MSF did not immediately respond to a request for comment. It says on its website it operates a maternity clinic at the hospital in one of Kabul’s poorest neighbourhoods.
A series of bloody attacks have taken place in the capital in recent months claimed by the Islamic State group.
On Monday, security forces said they had arrested three senior members of the so-called Islamic State group (IS), including a regional leader.
Last week, security forces killed and arrested several members of an IS cell that authorities said was responsible for several high-profile attacks in Kabul including one on a Sikh temple in March.
Roadside blasts in the capital on Monday, which wounded four civilians, were claimed by the group.
Afghanistan is also facing violence around the country from the Taliban even as the United States tries to usher in peace talks after signing a troop withdrawal agreement in February with the militants.
The Taliban say they are holding back from attacking urban centres and their operations are aimed at government security forces.
(FRANCE 24 with REUTERS)