This flood of neutrons may have imprinted an X-ray-like image onto the linen burial cloth, say the researches.
In addition, the radiation emissions would have increased the level of carbon-14 isotopes in the Shroud, which would make it appear younger.
"We believe it is possible that neutron emissions by earthquakes could have induced the image formation on the Shroud's linen fibres, through thermal neutron capture on nitrogen nuclei, and could also have caused a wrong radiocarbon dating," said Professor Alberto Carpinteri, from the Politecnico di Torino.
The scientists base the idea on research into piezonuclear fission reactions which occur when brittle rock is crushed under enormous pressure.
Neutron radiation is usually generated by nuclear fusion or fission, and may be produced by nuclear reactors or particle accelerators.
During the process, neutron particles are released from atoms.
A powerful earthquake could achieve the same effect, generating neutron radiation from stresses in the Earth, it is claimed.
Mark Antonacci, a leading expert on the Shroud and president of the Resurrection of the Shroud Foundation, is currently petitioning Pope Francis to allow molecular analysis of the cloth using the latest technology.
It is hoped that such an investigation will be able to confirm or rule out the radiation theory.
The Vatican has never said whether it believes the shroud to be authentic, although Pope Emeritus Benedict XVI once said that the enigmatic image imprinted on the cloth "reminds us always" of Christ's suffering.
Last year scientists at the University of Padua in northern Italy dated it to between 300BC and AD400 – still hundreds of years after Christ, who is believed to have died between 30-36AD.
Other scientists have previously suggested that neutron radiation may have been responsible for the ghostly image of a crucified man with his arms crossed.
However, no plausible explanation has been offered for the source of the radiation.
Now Carpinteri’s team have hypothesized that high-frequency pressure waves generated in the Earth’s crust during earthquakes are the source of such neutron emissions.