Negligence on the part of hospital authorities has been blamed for the fire on Saturday night.
Initial reports suggested it was caused when an oxygen cylinder exploded in the ward of Ibn al-Khatib hospital.
Iraq’s prime minister Mustafa al-Kadhimi fired key hospital officials hours after the incident.
Among the dead were at least 28 patients on ventilators battling severe symptoms of the virus, tweeted Ali al-Bayati, a spokesman of the country’s independent Human Rights Commission.
Firefighters rushed to battle the flames that raged across the second floor of the hospital. Civil defence teams put out flames until the early hours of the morning.
Ambulances transported dozens of wounded. The Health Ministry said at least 200 people were rescued from the scene.
Doctors at the scene were frazzled by the chaos unfolding around them. They said numerous burned bodies were carried out by paramedics from the hospital floor.
"I don’t know how many victims there are, there are so many burned bodies all over the place,” said Dr Sabah al-Kuzaie at the scene.
There were at least 120 patients in the hospital at the time of the fire, a doctor at the hospital said.
By midday on Sunday, relatives were still searching anxiously for unaccounted loved ones.
A statement from the Health Ministry and al-Kadhimi's office named the fired officials as director-general of the Baghdad Health Department in the al-Rusafa area and the director of Ibh al-Khatib Hospital and its director of engineering and maintenance.
After the fire first broke out, Al-Khadhimi held an emergency meeting at the headquarters of the Baghdad Operations Command, which coordinates Iraqi security forces, according to a statement on his Twitter account.
In the meeting he said the incident amounted to negligence.
"Negligence in such matters is not a mistake, but a crime for which all negligent parties must bear responsibility," he said.
He gave Iraqi authorities 24 hours to present the results of an investigation.
The fire came as Iraq grapples with a severe second wave of the coronavirus pandemic.
Daily virus cases now average around 8,000, the highest since Iraq began recording infection rates early last year.
At least 15,200 people have died of coronavirus in Iraq among a total of at least 100,000 confirmed cases.
The government is urging the public to get vaccinated, but demand has been low due to widespread mistrust of the health care system and the vaccines in particular.
UN envoy to Iraq Jeannine Hennis-Plasschaert expressed “shock and pain” over the incident in a statement and called for stronger protection measures in hospitals.