The incident occured on Tuesday morning at the Big Gossan mine, more than a kilometer away from Arizona-based Freeport-McMoRan's Grasberg mine, the largest open pit copper mine in the world, reports the Wall Street Journal.
Thirteen miners have been rescued but operations to save 23 miners are still ongoing.
PT Freeport Indonesia, the operator of the mine, said in a statement that the rescue process is "difficult" and will take some time to complete.
Company president Rozik B. Soetjipto said; "Our thoughts and prayers are with our fellow employees and their families as we proceed with rescue efforts."
The Big Gossan mine is one of three mines in the Grasberg minerals district an is adjacent to the current mill site. Production began at the site in 2010.
The other mines include Grasberg, which lies 4,000m above sea level, and the Deep Ore Zone underground mine.
Freeport has faced a number of challenges in recent years; more than 20,000 employers downed tools over wages for three weeks in early 2012 and three months in 2011.
Image: The Grasberg Mine is the largest gold mine and the largest open pit copper mine in the world. Photo: Alfindra Primaldhi.