Protesters stormed the legislature, breaking windows and fences.
The country's 1992 constitution, introduced after 35 years of dictatorship, strictly limits the president to a single five-year term.
But sitting President Horactio Cartes is attempting to remove the restriction and run for re-election.
Protesters were photographed smashing in windows of the congress building in Asuncion on Friday night and setting fire to the interior.
The AFP news agency said protesters "ransacked" the offices of those who backed the bill.