The deceased, identified as A Gangotri was found lying in a pool of blood in her apartment complex at Sujathanagar area by residents.
Gangotri was separated from her husband and living with her eight-year-old son with her brother, said Pendurthi police station inspector J Murali.
He said Gangotri has been under depression since she received a divorce notice from her husband ten days ago and was seeing a psychiatrist.
Police suspect that Gangotril might have committed suicide by jumping off her fifth floor apartment due to mental issues.