The girl, 16, believes she was doped after going to her boyfriend's house on Saturday and says she woke up in a different house, surrounded by the men.
Arrest warrants have been issued, including one for the boyfriend.
The assault has provoked an online campaign against what campaigners call a culture of rape in Brazil.
Conflicting versions of the story are still coming in, but the alleged rape is said to have taken place in a poor community in western Rio over the weekend.
According to a statement she is reported to have given to police, she woke up on Sunday, naked and wounded, and made her way home.
Only days later did she find out that some of the alleged rapists had put images of the attack on Twitter.
A 40-second-video was widely shared and followed by a wave of misogynistic comments, before the users' accounts were suspended.
Speaking to local media, the girl's grandmother said the family watched the video and cried.
"I regretted watching it. When we heard the story we didn't believe what was happening. It's a great affliction. It's a depressing situation," she told Folha de S.Paulo newspaper.
"She is not well. She is very confused. This was very serious."
The attack has shocked Brazil, says the BBC's Julia Carneiro, and campaign groups have been already been calling for protests over the coming days.
There has also been an outpouring of anger on social media, under the hashtag #EstuproNuncaMais (Rape never again).
A collective of journalists posted a satirical image of citizens donning devil's horns, condemning a rape victim for having provoked the attack.
The inscription reads "No to sexism", and the images, clockwise from top right: "But look at her clothes…", "She deserved it!", "16 years old and already has a son…", "Apparently she was on drugs".
The United Nations group UN Women issued a statement calling for authorities to investigate the case, but to respect the victim and not victimise her once more by invading her privacy.
Experts say many cases of rape in Brazil go unreported as victims fear retaliation, shame, and blame for the violence they have suffered.
Rape in Brazil
- 47,636 rapes were reported to the police in 2014
- It is estimated only 35% of rape cases are reported
- Rape of an adult is punishable by a prison sentence of between 6-10 years
- Sentence for rape of a minor is 8-12 years in prison