The victim, a 27-year-old musician, was staying on rent on the third storey of a building located on the Perry Cross Road in Bandra west.
The intruder entered the flat through the window and brandished a knife asking her to hand over her valuables, a senior police officer said.
The victim parted with some dollars, Indian currency and a camera. The accused then raped her, according to the complaint filed by the victim with Bandra police.
The incident occurred between 3.30 and 4.30 AM when the woman was fast asleep in her house, the police officer said, adding the accused ran away after committing the crime.
Police have spread a dragnet for the accused and have put on alert all their informers to trace the culprit.
After the incident, the victim came to Bandra Police station and filed a complaint alleging rape and robbery.
Police have registered an FIR and charged the wanted accused with offences of rape, house breaking and robbery.
Police also took the woman to a hospital for medical examination before registering the FIR, the officer said.
