The blaze left "19 dead, including 13 children, among them seven girls and six boys, in addition to four female teachers," the ministry said on its Twitter page, citing the country's health minister.
Two members of the civil defence also died in the fire, it said.
The fire at the capital's main Villagio shopping centre broke out at 11:30 am (0800 GMT), the ministry said, quoting state minister for interior, Abdullah bin Nasser Al-Thani telling reporters that the "public prosecution has taken charge of the investigation."
Footage posted earlier online showed black smoke billowing from the shopping centre as emergency vehicles rushed to the scene.
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