North Yorkshire Police were called by the ambulance service to the Cenotaph near Parliament Street at around 4.30pm on Sunday, March 6.
The 46-year-old man was taken to Harrogate District Hospital for treatment where he currently remains.
His injuries are not believed to be life-threatening.
Police are at the scene of the incident and are carrying out an investigation to determine how the man sustained his injury.
A spokesman for North Yorkshire Police said: “At this stage it is unclear how he came to be injured and officers need to establish if it was the result of an attack or if it was self-inflicted.”
Anyone with information is asked to call North Yorkshire Police on 101.