The demonstrations were held to express support for the United Liberation Movement for West Papua, which is vying for full membership in the Melanesian Spearhead Group.
Monday's protests came as West Papuans marked the anniversary of transferral of administration in the former Dutch New Guinea to Indonesia in 1963.
The independent West Papuan newspaper, Tabloid Jubi, reports that overall 1692 people were arrested.
Jubi reports that a researcher from Bern University in Switzerland was interrogated by police too.
The Jakarta Globe reported that over 500 arrests were made in a huge demonstration in Jayapura.
Reports from local media indicate that hundreds of others were arrested for demonstrating in cities like Merauke and Sorong, but also cities in other parts of Indonesia like Makassar and Semarang.
Last month, the head of Indonesia's Commission for the Disappeared and Victims of Violence, KONTRAS, said that last year more than 1,200 Papuans suffered from harassment, killings, torture and ill-treatment.
Haris Azhar said these abuses were often made by security forces against Papuans for exercising their right to freedom of expression, freedom of assembly and movement.