Police said the boys, reported to be between 15-16 years old, also recorded a video and circulated it on WhatsApp.
The accused and the victim lived in the same area and used to go to each others' homes to study together.
The boys were produced in court after which they were sent to a juvenile reform home, police said, adding that they were investigating further.
The girl was first raped on 8 November and she was assaulted several times since then, Shashank Sandbhor, a senior police officer in the city's Malad police station, told BBC Hindi's Ashwin Aghor.
"On 8 November, one of the accused telephoned the girl and invited her to his home, saying he needed help with his studies. Once she arrived, he and his friends gang-raped her," Mr Sandbhor said.
"The boys threatened the girl that they would upload the video on social media and raped her on several occasions thereafter. At the same time, they uploaded the video on WhatsApp," he added.
The girl's father is dead and her mother works abroad, so she lives with her sister, grandmother and aunt.
The video was extensively shared on WhatsApp and on Wednesday, someone sent it the girl's aunt, who spoke to the victim and got her to reveal what had happened, police said.
A case of gang rape has been registered and the stringent Protection of Children from Sexual Offences Act has been invoked against the accused, officials said.
The incident comes as a juvenile who was convicted in a high-profile case three years ago in which a young woman died after being gang-raped on board a Delhi bus, is due to be released from detention.
It has led to much public debate over India's sexual assault laws especially those that deal with juvenile offenders.
Four schoolboys in the western Indian city of Mumbai have been arrested for allegedly gang-raping their classmate.