The Vancouver-based miner says the accident happened Wednesday at the mine's processing plant.
Other details were not disclosed.
First Quantum said authorities had been informed and an investigation was expected to begin immediately.
"The mine has already commenced its internal investigation to determine the cause of the incident," the company said.
In addition to the Kansanshi project, First Quantum is also developing a copper-gold mine in Mauritania and the Ravensthorpe nickel mine in Australia.
On the Toronto Stock Exchange, the company's stock closed down 59 cents, or 2.74 per cent, Wednesday at $20.91.