They are stuck roughly 35 metres down the mine shaft, the governor of Geita province, Ezekiel Kyunga, told state media.
"We hope to find them alive," he said, noting that an area 20 metres deep had been cleared so far.
"The operations are being conducted with extreme caution to avoid causing other landslides that could complicate things."
According to the Tanzanian press the workers have been stuck in the Chinese-operated mine since Friday.
The collapse of mine shafts is frequent, with miners often lacking the tools and materials considered necessary to operate safely.
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