Two men have been arrested. They attacked the couple, who had boarded the minibus in the Copacabana area of the city, police say.
The couple's identities and nationalities have not been disclosed.
Curbing violence is a major priority for the authorities in Rio, which is hosting the football World Cup next year and the 2016 Olympics in 2016.
Police say two suspects have been arrested: Jonathan Foudakis de Souza, 20, the bus driver, and Wallace Aparecido de Souza Silva, 22.
Dumped outside Rio
The suspects told other passengers to get off the bus, and drove it to the outskirts of Rio de Janeiro, police said,
The woman was raped repeatedly as the minibus crossed the long bridge over the Guanabara Bay in Rio.
Her boyfriend was handcuffed and badly beaten.
The couple was dumped in the nearby city of Itaborai, after being forced to use their credit cards for shopping and to withdraw money from cash machines, the police report says.
The two alleged culprits were arrested hours after the attack.
Police are looking for a third man. He was contacted by mobile phone, boarded the bus outside Rio and also raped the woman, police say.
Robberies are a common occurrence on buses in Rio de Janeiro and other big Brazilian cities, but the violence and audacity of this attack has shocked local media.