Paul and Rachel Chandler were heading for Tanzania from the Seychelles in their 38ft yacht, the Lynn Rival.
“The British couple are in our hands now. We captured them as they were touring in the Indian Ocean,” a pirate called Hassan told the Reuters news agency.
The pirate added that the two captives, who are both in their 60s, were healthy and that a ransom demand would follow.
The Foreign Office said it was urgently investigating after the ship reportedly sent a distress signal on Friday. It has not been heard from since.