The girl, who was last seen on the night of November 8 by other hostel inmates, did not answer calls from her mother this morning, a police official said.
"The girl's mother later called one of the hostel inmates and requested to look for her daughter," the official told PTI adding that the student, along with others, went to check her room and found her hanging from the ceiling fan.
The inmates broke open the door and informed police, who removed the body to the Government Royapettah Hospital.
The student's family in Kollam was also informed.
The official said no suicide note was found and the preliminary probe indicated that the girl was concerned about her academic performance.
In a brief statement, IIT Madras expressed deep grief and sadness over the girl's death.
"IIT Madras faculty, staff and students extend their deepest condolences to the family, friends and other near and dear ones of the deceased student.
This is indeed an irreparable loss to the institute and the family. May her soul rest in peace."
Police have been informed and the institute is cooperating with the authorities, the premier institution said.