The incident happened at Landolam settlement near the mining town of Lihir.
The women, from the Highlands region, are in hiding as police investigate.
Lihir Police Station Commander Senior Inspector Elisha Taksir says the three women were suspected to have committed sorcery on a teenage girl from Landolam village.
The matter was reported to police but while police investigations were still underway, the complainant decided to take the matter into his own hands.
The sick girls father mobilized his men from the settlement who are non New Irelanders and hunted down the three women.
The women were physically attacked, tied to a tree, and burnt with hotel metal rods.
The matter has been reported to police but arrests are yet to be made.
PSC Taksir says the incident is the first of its kind to be reported in the province. NBC