Police said the woman aged in her twenties reported that she had been attacked as she was walking from Windsor Terrace to Esk Terrace between 3.05am and 6.20am on Sunday (April 15).
The suspect is described as a man wearing a dark blue hooded top.
Detectives conducted enquiries on Sunday and have spoken to nearby residents as part of the ongoing investigation.
They are appealing for people to come forward who may have seen the victim and the suspect between 4am and 6:30am on Sunday in Windsor Terrace, Esk Terrace and neighbouring streets in Whitby.
Anyone with information is asked to contact North Yorkshire Police on 101, select option 2 and ask for the Scarborough Serious Crime Team. Or email DC Jon Kenworthy at [email protected]
Or call Crimestoppers anonymously on 0800 555 111. Please quote reference 12180063948 when passing on information.