She was swimming near Ascension Island, part of the territory of St Helena, and one source told the Times her husband punched the shark to scare it away.
The woman, who works for the St Helena government, was treated in hospital locally, but later airlifted to the UK.
St Helena is a British Overseas Territory, 1,150 miles (1,850km) off the west coast of Africa.
The government has warned swimmers entering the water in the area that they do so at their own risk.
The remote islands of St Helena, Ascension Island and Tristan da Cunha lie midway between Africa and South America, and though far from each other, they form a single territorial grouping under the sovereignty of the British Crown.
In the 1600s, the English East India Company was given a Royal Charter which allowed it to colonise the island, but St Helena is perhaps best known as the destination to which Napolean Bonaparte was exiled in 1815 after his defeat at the Battle of Waterloo.
Today, the islands have a combined population of less than 6,000, and are linked to the outside world by a Royal Mail Ship, the St Helena, which makes a five-day journey from South Africa, every three weeks, carrying passengers and supplies.