The girl, hailing from Darjeeling in West Bengal, was brought to the city by the family from Assam, who runs a consulting agency in Bangalore, they said.
She was allegedly beaten by the couple, police said.
As the girl fell unconscious on Thursday, she was first taken to the National Institute of Mental Health and Neurosciences by the couple and was later shifted to a private hospital, they said.
The girl was later shifted to the government-run Vani Vilas Hospital, police said, adding, "she is now out of danger".
The couple was arrested on Friday and booked under various sections of the Indian Penal Code, including 326 (voluntarily causing grievous hurt with dangerous weapons or means), they said.
Tata-SIA may sport Vistara brand name
WBPCC chief criticises Amit Mitra's remarks against Tata
Poachers have hunted down 193 rhinos since 2001 in Assam
Inculcate habit of winning all polls, says BJP chief Amit Shah
Hawt couture! Richa, Aditi scorch the runway