The aircraft went down in the Estancia La Mocha area of Puerto Antequera Saturday night, killing Oviedo, his bodyguard and the pilot.
The Interior Ministry said it had launched an investigation and would consult with international experts to determine the cause of the crash.
Oviedo, a former military general, was killed shortly after a campaign appearance in Concepcion, La Nacion said in a translated report. He was flying in a chopper owned by a Brazilian businessman.
Oviedo was considered instrumental in the 1989 coup that led to the current democratic government in Paraguay, La Nacion said.
President Frederico Franco issued a statement lamenting Oviedo's death and declared a three-day mourning period during which presidential campaigning would be suspended.