The woman was plucked out of the Atlantic around midnight on Saturday some 500 metres (yards) from the coast, shivering and clinging to a small bag, said the head of the Funchal port authority, Felix Marques.
Fishermen came to the rescue after they were alerted by her cries for help, he added.
According to the Portuguese daily Correio da Manha, the woman and her husband had earlier disembarked from the Marco Polo at Portugal's Funchal port and decided to fly back to Britain after having an argument.
But upon arriving at the airport, the British woman reportedly saw the Lisbon-bound cruise liner passing near the shore and wrongly thought her husband may have been back on board.
She jumped into the water around 2000 GMT and started swimming towards the ship, Marques said.
She was rescued some four hours later and taken to a hospital in Funchal with symptoms of hypothermia.
Local SIC television said the woman's husband had not returned to the ship but had taken the first flight home.