One of the officers shot in Wednesday's attack was in critical condition, officials said.
Police have been combing the jungle around the sprawling Grasberg complex in the hunt for those behind the attacks, but so far no arrests have been made.
The Grasberg complex is majority owned by Freeport-McMoRan Copper & Gold Incorporated, based in the US state of Arizona.
The complex employs 20,000 people and includes the world's largest gold mine.
On Tuesday a Freeport vehicle also came under fire, but no one was hurt in the incident.
Papua, a poor and mountainous province, lies some 3,400km east of the Indonesian capital, Jakarta.
It is home to a 40-year-old insurgency that has denounces the Freeport mine as a symbol of outside rule.
Many Papuans are resentful because the mine earns billions of dollars in profit from the region's natural resources, little or none of which makes it back to the local community.
Indonesian media, however, have quoted rebels as denying involvement in the shootings, and Indonesian officials and experts have said they doubt whether the rebels have the organisation or unity to mount coordinated attacks.