Bolsonaro, who has yet to concede to leftist incumbent Lula, left Brazil after refusing to comply with a Supreme Court order to surrender his passports.
The location of Bolsonaro, his wife and two daughters was not immediately clear. One source close to the family said they had landed in Florida, but declined to say where.
Bolsonaro's departure threatens to deepen a rift between the two most populous nations in the Americas. Lula has accused Washington of colluding with the Bolsonaros to put them back in power.
Trump has previously alleged Flavio's father, former president Jair Bolsonaro, was a victim of judicial persecution in Brazil.
The elder Bolsonaro also went to the United States after refusing to concede to Lula in 2022, when former US president Joe Biden was in office. He eventually returned but was later given a 27-year sentence for plotting a coup after his supporters stormed government buildings in Brasilia.
Trump made no mention of Bolsonaro's departure in comments to the press on Monday but said the Brazilian vote "looked like another rigged election".
Lula's office did not respond to a request for comment.
Bolsonaro was favoured to win Sunday's presidential election but ended up losing in a shock result to Lula.
On Monday, he was given 24 hours to surrender his passports as part of a money laundering probe in which he denies wrongdoing but his documents were cancelled after the deadline lapsed.
Bolsonaro, who loses his immunity from prosecution when his Senate term ends in February, previously said he had no plans to flee.
"I have never thought about leaving the country," he said.
"I will hand over my passports and defend myself against this travesty, which is a clear attempt to intimidate me."
Brazil's Minister of Institutional Relations Jose Guimaraes commented on reports of Bolsonaro leaving in an interview with CNN Brasil.
"I have no confirmation from the federal police or oversight bodies," he told the news outlet.
"But this speaks a lot about our opponent's lack of preparation to govern the country."
Flavio Bolsonaro initially asked for the election results to be annulled after an evening of chaos at some polling places that prompted authorities to extend voting by two hours.
On Monday, he urged the electoral court to investigate alleged election fraud and nullify Lula's and Vice President Geraldo Alckmin's candidacies, which the electoral court has never done before.
To overturn the result, Bolsonaro would have to present evidence of fraud affecting Lula's 4.4 million-vote margin and convince the eight-member electoral court before the results are certified on December 18.
Lula, who turned 81 on Tuesday, received more than 64 million votes, compared with fewer than 60 million for Bolsonaro, a margin of nearly four per cent.
It remains unclear how Bolsonaro was able to leave the country while he was facing a 24-hour deadline to hand over his passports.
with AP
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