It was discovered at Holme-next-the-Sea at around 1.30pm on Monday.
The law states that porpoises, whales, dolphins and sturgeons are “Fishes Royal” and belong to King Charles when in UK waters.
Because of this, Hunstanton Coastguard was called to take measurements and details of the porpoise to pass along to the National History Museum.
A spokesman for the coastguard team said the porpoise was “believed to be a juvenile, almost fully grown, male harbour porpoise”.
There were no signs of injury.
“The BDMLR (British Divers Marine Life Rescue) team and CSIP (Cetacean Strandings Investigation Programme) will be involved in the recovery of the porpoise and the subsequent necropsy to establish the cause of death,” he added.