The crime raised fears ahead of World Youth Day in July, when the city is set to welcome Pope Francis and some 2.5 million young people. Brazil is also hosting the 2014 World Cup and 2016 Summer Olympics.
Two male suspects in the case, aged 20 and 22, were detained over the weekend, a police spokesman said. A third suspect was detained late on Monday in the Rio metropolitan area, according to local media.
"She is a US national and he is French; they were studying in Rio," a French consular source informed, in reference to the victims.
The American, 21, and the Frenchman, 23, according to local media, boarded a minibus around midnight on Saturday in touristy Copacabana headed to Lapa, a trendy area home to popular bars and dance clubs.
Two men who also boarded the minibus ordered the rest of the passengers to get off and handcuffed their victims.
They then proceeded to beat the young man with a metal bar and rape the young woman as they rode around the city, the special police for aid to tourists (DEAT) said.
After seeing photographs of two of the detained suspects, a young Brazilian woman who was raped on March 23, also in a minibus, identified them as her assailants, DEAT added.
The driver of the minibus may also have taken part in the rape of the American, local media reported.
The G1 news website said the Frenchman suffered an eye hemorrhage and a fractured face while the American's nosed was broken during the assault.
Minibuses are part of Rio's transportation network and, in a city of six million inhabitants, are often considered alternative means of getting around.
While some do have permits, many others are illegal and often take to streets in poor condition and packed with people.
Violence has declined in Rio following efforts by authorities to reclaim dozens of favelas once controlled by drug traffickers or militias, but the city remains rough when compared to Europe or the United States, with huge disparities between the rich and the poor.