According to the police, the event occurred the day before in a central region of the country, in the district of Mumbwa, about 150 kilometers west of this capital, Lusaka.
Authorities said rescue operations were underway and it was unclear exactly how many miners were left underground.
The cause of the collapse is so far unknown, but nine bodies were recovered from the site and a tenth person died at a hospital, where five others who were injured are being treated.
Collins Nzovu, a government minister and local member of parliament, said some 20 miners were missing.
Informal mining is very common in these African regions, where dozens of workers die as they try to seek a livelihood in this type of work without any safety controls.
Last year, dozens of people died in Zambia when an informal copper mine collapsed due to a landslide in the town of Chimgola, in the north of the country, according to economic analysts.
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