The protesters were enraged by recent changes to Senate rules that would allow President Horacio Cartes to seek re-election. Paraguay's 1992 Constitution limits presidents to one term.
Some demonstrators vandalized offices and hallways throughout the congressional building in Asunción as flames spread through the structure. Police vehicles also were targeted.
Firefighters rushed to the scene while riot police showed up with water tanks. Police fired rubber bullets at some of the protesters.
Interior Minister Miguel Tadeo Rojas said Saturday that authorities had opened an investigation into the protester's death and have detained one police officer in the killing. He lamented the death of Rodrigo Quintana and sent condolences to his family
A Senate meeting that was to be held Saturday morning was canceled.
The violence stems from the ruling Colorado Party's decision to create an alternative Senate with the goal of passing laws that would allow Cartes to seek a second term. Protesters indicated they will stop demonstrating once they get a commitment from Cartes that he will not seek a second five-year term.
On Tuesday, a group of 25 senators began holding what has been called "parallel sessions." Julio César Velásquez of the Colorado Party proclaimed himself Senate president and, with the help of two dozen other senators, began making changes to the body's rules and procedures.
The group held a secret vote early Friday in favor of the re-election bill. The vote was not held on the main Senate floor but in an office at the congressional building.
Paraguay's 45-member Senate requires a simple majority of 23 votes to pass legislation, meaning the group holding parallel sessions technically have two more votes than required.
Most of the senators involved in the parallel sessions were members of the Colorado Party, but some from the opposition also joined in.
Paraguay lived under a dictatorship for 35 years. Alfredo Stroessner, a Paraguayan military officer, took power after an armed coup in 1954. His rule ended in 1989.
In an interview with CNN, Sen. Lilian Samaniego of the Colorado Party rejected accusations that her political organization is trying to establish a dictatorship.
"I don't know what dictatorship they're talking about," Samaniego said. "Dictatorship is what these opposition senators and representatives, unfortunately with some dissidents from the Colorado Party, would like to establish because they want to decide for the people. And we want the Paraguayan people to decide for themselves."
On Thursday, Senate President Roberto Acevedo asked Paraguaya's Supreme Court to issue an injunction to annul modifications made by the rogue group to the Senate rules and procedures.
Sen. Carlos Amarilla of the Liberal Party told CNN affiliate Telefuturo that, legally speaking, "the only (Senate) president is Sen. Roberto Acevedo. Any other alternative would have to wait until June 30 to elect a new leadership by majority."