The man’s wounds were not believed to be life-threatening, Royal Cayman Islands Police said.
Officers could not immediately confirm the location where the man was stabbed and did not state if they were able to interview the victim.
The stabbing victim was the second mystery attack patient to appear at the hospital so far this month.
On 1 December, a shooting victim was dropped off there after being injured at an unspecified location. That man, Frank McField, had to be taken to hospital in Miami after a bullet broke a bone in his right leg.
Police provided no further information about Saturday’s stabbing victim.