Shyam P Salla, the accused, fled from the spot after the act. He was arrested late in the evening, police said.
The victim, Rajashree Mehotra, was married but staying with her brother Shyam and their mother due to a strained relationship with her husband, a senior police official said.
Shyam often quarrelled with her as she was not staying with her husband and in-laws. The two had a heated exchange on the issue this afternoon and Shyam allegedly stabbed Rajashree with a kitchen knife.
The siblings' father, who died a few years ago, worked in the Navy. Following his death, their mother got a job in the defence force and thus they stayed in an official quarters.
Cuff Parade police are probing the case.