Police said the "extremely distressing" assault took place at a property in the Eliburn area of Livingston, West Lothian, at about 3.30am on Wednesday.
The 27-year-old woke to find the man in her home. He indecently assaulted her and left the property afterwards. The woman contacted police immediately.
Detective Superintendent Pat Campbell said: "This was an extremely distressing assault for the woman, who was woken in the night by an intruder. We would like to appeal to any person within the vicinity at the time who may have any information regarding this incident to contact police immediately."
The suspect is described as white, 20 to 30, 5ft 9ins to 6ft, with a medium build and short dark brown hair.