Pirates boarded the Chandlers' yacht, the Lynn Rival, while they slept
The crew of a UK military ship watched as a British couple were forced off their yacht by Somali pirates but were ordered not to open fire.
Paul and Rachel Chandler, aged 59 and 55, from Kent, were transferred to another ship on 28 October, five days after they were originally hijacked.
The MoD said the Royal Fleet Auxiliary tanker - the Wave Knight - had not wanted to endanger the couple's lives.
The Chandlers had been travelling to Tanzania from the Seychelles.
Details of the Navy operation were leaked to the press by an anonymous crew member of the Royal Fleet Auxiliary ship.
The crew member revealed that the RFA Wave Knight had come within just 50ft (15m) of the couple's yacht, the Lynn Rival, at one point.
A MoD spokesman said: "Every effort was made by the Royal Navy and the international maritime fleet to locate the Lynn Rival.
"We did everything we could possibly do without further endangering the lives of Paul and Rachel Chandler.
"We do not comment on operational detail but RFA Wave Knight did very well under the circumstances."
The replenishment tanker was carrying 75 merchant seamen and 25 Royal Navy sailors, as well as a helicopter, at the time of the incident.
An official account of the kidnap released last month said only that a Royal Navy vessel had found the couple's yacht empty, without disclosing that the couple were within sight at the time.
In a phone call on 29 October, the couple, from Tunbridge Wells, said they were initially moved from their yacht to a container ship, the Kota Wajar, which had also been seized by the pirates.
It is thought they were then moved to another ship anchored off the eastern coast of Somalia before being taken to the mainland.
The pirates have issued a $7 million (£4.3 million) ransom demand but the British government has insisted it will not make any ransom payment.