The Iraqi Health Ministry said the babies were in the pre-term birth unit in Yarmouk Hospital and died of suffocation.
A preliminary report provided by the Civil Defense indicates the fire was caused by an electrical short circuit.
Officials said twenty-nine women delivered babies at Yarmouk hospital Tuesday night. They were all transferred to other hospitals in the Iraqi capital.
No other details were immediately available, but there have been a number of electrical fires at state institutions and shopping centres in Iraq in recent years.