The fire was likely caused by a malfunctioning air conditioning unit in the early hours of the morning, local rescue officials told dpa on Wednesday.
Only one of the newborns in the ward was rescued, they said. The fire was now under control.
The maternity ward is part of the gynaecology department at the Pakistan Institute of Medical Sciences, a state-run hospital.
Prime Minister Shehbaz Sharif expressed sorrow over the deaths and ordered an immediate investigation.
"Those responsible should be identified, and the strictest action should be taken," Sharif's office said in a statement.
"A tragedy involving children is an irreparable loss," Sharif said.
The ward was cordoned off and ambulances were seen outside the hospital building, according to a Reuters witness.
PIMS, centrally located in Islamabad where former prime minister Imran Khan was briefly treated last week, is one of the main public hospitals of the city.
Television footage from Geo News showed heavy smoke and firefighters working at the scene.
The broadcaster said an investigation would be launched into the further causes of the fire.
Public hospitals in Pakistan are unpopular because of lower standards, with those who can afford it opting for private clinics for better care. Lax safety standards have repeatedly led to tragedies in Pakistan.
with AP, Reuters
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