The Sunday game between Olimpia and Cerro Porteno, both from the capital Asuncion, was halted after 29 minutes on the orders of the referee.
The police said a group of Cerro Porteno fans who arrived late, some without tickets, forced their way into the venue.
"Once in the stands, the fans began throwing rocks and bottles filled with water or urine," the capital's police chief Hector Fernandez, told a press conference.
Police responded by firing rubber bullets and tear gas into the stands, forcing hundreds of spectators to flee onto the pitch, television footage of the incident showed, with smoke engulfing portions of the stands.
A 22-year-old police officer suffered a broken nose and other facial injuries that would require surgery, said David Torales, director of the Rigoberto Caballero Police Hospital.
Video of the attack on the officer went viral on social media.
Security forces said at least six officers had been injured.
Most of those treated in hospital had minor injuries, medics said.
The match between Olimpia, which leads Paraguay's top football division just ahead of Cerro Porteno, was played before 40,000 spectators.
Police said they were working to "identify those who instigated the conflict so that they may be sanctioned and barred from attending future sporting events."
The Paraguayan Football Association (APF) holds that a team must forfeit a match if its supporters force the game to be suspended.
Olimpia President Rodrigo Nogues said his club will seek to be awarded the three points from the APF disciplinary tribunal.
Cerro Porteno President Blas Reguera, meanwhile, said Olimpia was responsible for stadium security, citing their status as the match's organising club.