The bird was found by a man in Surrey, southern England while he was cleaning out a disused fireplace at his home earlier this month.
The message, a series of 27 groups of five letters each, was inside a red canister attached to the pigeon's leg bone and has stumped code-breakers from Government Communications Headquarters (GCHQ), Britain's main electronic intelligence-gathering agency.
"Without access to the relevant codebooks and details of any additional encryption used, it will remain impossible to decrypt," a GCHQ spokesman said.
The message is consistent with the use of code books to translate messages which were then encrypted, according to GCHQ, one of Britain's three intelligence agencies.
However without knowing who the sender, "Sjt W Stot", is or the intended destination, given as "X02", it is extremely difficult to decipher the code, GCHQ said.
Although the code books and encryption systems used should have been destroyed, there is a small chance that one exists somewhere.
A spokesman for GCHQ said it was "disappointing" that the message brought back by a "brave" carrier pigeon cannot be read.
He added: "It is a tribute to the skills of the wartime code-makers that, despite working under severe pressure, they devised a code that was undecipherable both then and now."
The Curator of the Pigeon Museum at Bletchley Park, north of London, Britain's main code-breaking centre during World War Two, is also trying to trace the identity numbers of the pigeon found in the message, according to GCHQ.
Pigeons were used extensively in the war to carry vital information to Britain from mainland Europe. Flying at speeds of up to 80 km per hour, they can travel distances of up to 1,000 km but were vulnerable to hungry hawks and bored soldiers who used to take pot-shots at them as they flew overhead.
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