The man, who is in his early 20s and of a slim build, suffered serious injuries to his face in an incident outside Lloyds Bank on St Nicholas Street at about 12.30pm on Tuesday April 6.
The injuries were so severe that they required hospital treatment.
Officers are appealing for the public's help to establish what happened on a busy town centre street.
Scarborough Police are asking that anyone who witnessed the incident or can offer any information to come forward.
Anyone with information that could assist the investigation should contact North Yorkshire Police on 101. You can also email [email protected]
If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
Quote the North Yorkshire Police reference number 12210092607.