The victims' nationalities were not immediately released, but local media reports have said the woman is American.
The incident raises new questions about security in Rio, which has cracked down on once-endemic drug violence in preparation for hosting next year's football World Cup and the 2016 Summer Olympic games. The city will also be playing host to World Youth Day, a Roman Catholic pilgrimage expected to draw some 2 million people in late July.
The attack also drew comparisons with the fatal December beating and gang rape of a young woman on a New Delhi bus. Six men beset a 23-year-old university student and male friend after they boarded a private bus, touching off a wave of protests across India demanding stronger protection for women.
In the Brazil attack, the police statement said the suspects forced other passengers to get out of the van and then sexually assaulted the female tourist inside the vehicle, which was one of a fleet of vans that serve bus routes and seat about a dozen people.
During the alleged assault, the tourists were driven to the poor suburban neighborhood of Sao Goncalo, where the two suspects were apprehended, the statement said.
Reports said the two foreigners had been studying Portuguese in Rio for about a month and that both left Brazil following the attack.
The police statement said that one victim's cellphone was found in the suspects' possession. The suspects had also used a debit card belonging to one of the victims at two gas stations, it said.
The Globo television network broadcast surveillance camera images of two men filling up the white van and showed police images of a metal bar the suspects are thought to have used to beat and intimidate the victims.
The victims positively identified the two suspects, and a Brazilian woman has said she was assaulted by the men on March 23, the statement said.
In an interview with Globo television, commanding officer Alexandre Braga, who heads the Rio police unit specializing in crimes against tourists, said the suspects had gone on a sex crime spree.
"The characteristics of both crimes, both the Brazilian case and the one with the foreigners, lead us to believe that they (the suspects) wanted to have a 'party of evil,' in quotes," Braga said. "The principal motive appears to have been the satisfaction of their lust."
He added that the robbery and other crimes appear to have been "secondary."
Multiple calls to police seeking further details on Monday were not immediately returned.
In Brazil, more than 5,300 cases of sexual assault were reported between January and June 2012, according to the country's Health Ministry.