The unnamed man, reported to have been an expatriate and an experienced diver, was said to have been diving with his nephew when he became unresponsive.
He was taken ashore in a dive-boat, but reportedly went into cardiac arrest. Paramedics had already been called and attempted CPR, but the diver was pronounced dead at the scene.
The Atlantic Museum features the works of British underwater sculptor Jason deCaires Taylor in the form of 300 life-sized figures, and lies no more than 12-15m deep off Playa Blanca in the south of the island.
In September two visiting British divers died in the Canary Islands, one of them, 54-year-old Johnny Walker, at the start of a dive at the same site, as reported on Divernet.
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