The man entered the property on Balderstone Hall Lane, Mirfield, while it was empty, at around 2.40pm on Friday (May 26).
The intruder went downstairs when the victim returned home, swore at her and brandished the knife, before making off from the scene.
Officers at West Yorkshire Police say they want to speak to a white man around the age of 50, in connection with the incident,
He was wearing a khaki jacket, had a bottle of Lucozade in his pocket and was carrying a black draw string bag.
He had grey hair with a bald patch on top, grey stubble on his face and “possibly some missing teeth”.
Witnesses are asked to call Huddersfield CID on 101 quoting log 1071 of 26 May.