Much of Iraq's health care system is in poor condition after years of conflict and angry relatives of the victims have been protesting outside the facility.
The cause of the fire at the al-Hussein hospital is unclear, but reports said it began after an oxygen tank exploded.
Iraqi PM Mustafa al-Kadhimi ordered the arrest of the head of the hospital.
The speaker of the Iraqi parliament, Mohammed al-Halbousi, tweeted that the blaze was "clear proof of the failure to protect Iraqi lives, and it is time to put an end to this catastrophic failure".
Reuters news agency reported clashes between demonstrators and police at the scene, and two police vehicles set ablaze.
The new ward had space for 70 beds and was built just three months ago, medical officials told the Associated Press news agency. A health official said that at least 63 people were inside when the fire began.