Iraq's interior ministry said that 61 people died, most of them from suffocation, in the fire that broke out late on Wednesday in the city of Kut in Wasit province.
Among the dead were 14 charred bodies that remained unidentified, it said.
Civil defence teams were able to rescue more than 45 people who were trapped inside the building, the statement said.
The mall, which had opened only a week earlier, was in a five-storey building that also contained a restaurant and supermarket.
The state-run Iraqi News Agency reported that people remained missing.
Photographs and videos on local media showed the building fully engulfed in flames.
Provincial Governor Mohammed al-Mayyeh declared three days of mourning.
He said the cause of the fire was under investigation but that legal cases were filed against the building owner and mall owner.
"We assure the families of the innocent victims that we will not be lenient with those who were directly or indirectly responsible for this incident," al-Mayyeh said.
Iraqi Prime Minister Mohammad Shia al-Sudani said in a statement that he had directed the interior minister to go to the site of the fire to investigate and take measures to prevent a recurrence.
Poor building standards have often contributed to tragic fires in Iraq.
In July 2021, a blaze at a hospital in the Iraqi city of Nasiriyah that killed between 60 to 92 people was determined to have been fuelled by highly flammable, low-cost type of "sandwich panel" cladding that is illegal in Iraq.
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