Five men have been convicted following a raid on a military stockpile in the country, according to the Australian Broadcasting Corporation.
Since 1960s, many Papuans were involved in separatist insurgency against the Indonesian government.
The move to free the prisoners comes after the international community unsuccessfully begged Widodo to grant clemency to two Australians on drug charges.
Australians Andrew Chan and Myuran Sukumaran were executed in Indonesia in late April alongside six other men on drug charges.
They were arrested in 2005, trying to smuggle 18 pounds of heroin from Indonesia to Australia.
The international condemned the executions, and Australia recalled its ambassador to Indonesia.