The incident occurred late on Monday at one of five production blocks in the Grasberg Block Cave underground mine in Central Papua, the company said.
The location of the seven workers is known and they are believed to be safe, Freeport said, adding that rescue crews are working to clear the area for a safe and swift evacuation.
Bahlil Lahadalia, Indonesia's mining minister, said on Tuesday his team would go to the area for checks and give updates once they have returned.
Freeport operates Grasberg, one of the world's largest gold and copper mines, and had been building a smelter in Indonesia. The smelter was damaged by a fire last year and was shut down.
Three-month copper on the London Metal Exchange pared earlier losses to stand 0.08% lower at $9,907 per metric ton by 0918 GMT.
Freeport Indonesia estimated that its copper concentrate output would reach 2.964 million metric tons in 2025.
