At least 700 prisoners are reported to be involved in the uprising, which began on Sunday morning.
The prisoners are said to be unhappy about how the prison is run, as well as about food and hygiene there.
The trouble broke out when warders delivering food to inmates were reportedly overpowered.
As many as 1,000 prisoners then took over parts of the jail, ransacking and setting fire to much of it.
The rioting prisoners have their faces covered with improvised balaclavas.
The leaders of the rebellion are holding at least two prison guards hostage.
Violence between prisoners most likely involves members of rival drug gangs.
Negotiations are under way to put an end to the uprising, which has led to the destruction of most of the penitentiary, according to O Globo newspaper.
The Security Secretary of Parana State, Maria Tereza Uille Gomes, has travelled to Cascavel to take over the negotiations.
Brazil has the world’s fourth largest prison population, with half a million inmates in facilities meant to hold 300,000.
Across the country, many poorly resourced jails are in effect run by powerful crime gangs.
Earlier this year the UN High Commissioner for Human Rights, Navi Pillay, called for an investigation into the high number of violent deaths in Brazil’s prisons after previous riots at a jail in the north of the country left dozens of people dead.
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