The animal was found at the tide line below the beach huts by Hugh Stebbing, on January 28.
The incident was reported to Rother District Council who said it was illegal to remove these animals without permission.
A council spokesman said: “The picture shows a porpoise which was reported to us on Wednesday, January 28 as being washed up on Cooden Beach, but following an extensive search of the beach there was no sign of this creature.
“Despite being mammals, cetaceans such as dolphins, porpoises and whales are classed as ‘Royal Fish’ and it is illegal to remove them without permission from the Receiver of Wreck at the Marine and Coastguard Agency.”
The incident comes less than two weeks after a dead horse washed up on a beach in St Leonards.