Police told BBC Hindi that the child was killed on the instructions of a "sorcerer" to "cure" a paralysed man.
The man's brother and sister have been arrested on charges of abducting and murdering the girl.
The alleged sorcerer told them it was the only way to undo "black magic" affecting their sibling, police said.
A 17-year-old boy has also been arrested for helping to abduct the girl, police said.
"There are a few more people who have abetted the crime. We are investigating it from all angles. So more arrests cannot be ruled out," senior police officer B Ramesh told BBC Hindi's Imran Qureshi.
The murder was discovered after residents discovered the body of the girl inside a bag. They also found materials which police believe were used to conduct "black magic" rituals.
As news about the incident spread, a mob gathered outside the brother and sister's home and began throwing stones. Police had to use force to disperse the gathering.