The incident happened around 3 a.m. April 13 on the in the East Village.
Authorities say the suspect snuck into the 32-year-old victim's apartment, possibly through a door she forgot to lock when she got home.
The woman woke to find the man standing on her bed. He then sexually assaulted her, but fled when she struggled and screamed.
Police believe the man may have gone door to door inside the building, checking for unlocked doors.
The suspect is described as a Hispanic male in his 20s, standing about 5-foot-4 and weighing 160 pounds.
Anyone with information is asked to call Crime Stoppers at (800) 577-TIPS (8477).
