Dr. Ahmed al-Rudaini, a spokesman for the Iraqi Ministry of Health, said the fire broke out on Wednesday morning at Yarmouk Hospital killing 11 newborns and injuring at least 25 people.
Seven other children and 29 women were rescued they were transferred to a nearby hospital, the Iraqi health ministry said in a statement.
Baghdad authorities quickly sealed off the hospital and were barring then media from the site.
The initial investigation indicated it was an electrical fire.
Some relatives gathered outside claimed their babies were still missing and demanded an answer from authorities.