The company said the slippage occurred in the early hours of January 23, on the slope of the northern zone of the openpit mine at the mining hydrometallurgical complex in the Seville province.
It said the slippage had not caused harm to any people, nor had any impact on any third party facilities or land.
"The company has immediately activated the established safety and environmental emergency procedures, evacuating the area and isolating the incident," the company said.
"At the present time, production in the hydrometallurgical plant has been temporarily suspended while investigations are being conducted."
First Quantum said it was in communication with relevant administrations and was taking "all the necessary measures" to resolve the incident.
Las Cruces had produced 70,738 tonnes of copper cathode in 2018, according to First Quantum's preliminary results released this month.
The figure was below 2017's 73,664t and below guidance of 72,000t.
A planned shutdown in September followed by a failure in the grinding thickener had reduced equipment availability by 14 days, the company said in October.
First Quantum shares closed down 0.7% yesterday to C$12.52, towards the lower end of its 52-week range of $9.45-$23.05 and capitalising it at $8.6 billion.