Spartel Island now lies 60m under the sea in the Straits of Gibraltar, but some think it once lay above water.
The finding adds weight to a hypothesis that the island could have inspired the legend recounted by the philosopher Plato more than 2,000 years ago.
Evidence comes from a seafloor survey published in the journal Geology.
Marc-André Gutscher of the University of Western Brittany in Plouzané, France, found a coarse-grained sedimentary deposit that is 50-120cm thick and could have been left behind after a tsunami.
Dr Gutscher said that the destruction described by Plato is consistent with a great earthquake and tsunami similar to the one that devastated the city of Lisbon in Portugal in 1755, generating waves with heights of up to 10m.
The thick "turbidite" deposit results from sediments that have been shaken up by underwater geological upheavals.
It was found to date to around 12,000 years ago - roughly the age indicated by Plato for the destruction of Atlantis, Dr Gutscher reports in Geology.
Spartel Island, in the Gulf of Cadiz, was proposed as a candidate for the origin of the Atlantis legend in 2001 by French geologist Jacques Collina-Girard.
It is "in front of the Pillars of Hercules", or the Straits of Gibraltar, as Plato described. The philosopher said the fabled island civilisation had been destroyed in a single day and night, disappearing below the sea.
Sedimentary records reveal that events like the 1755 Lisbon earthquake occur every 1,500 to 2,000 years in the Gulf of Cadiz.
But the mapping of the island carried out by Dr Gutscher failed to turn up any manmade structures and also showed that the island was much smaller than previously believed.
This could make it less likely that the island was inhabited by a civilisation.
Story continues news.bbc.co.uk