The yacht, en route from Bahrain to Dubai, was stopped by Iranian naval vessels on November 25, he said in a statement.
The five crew members were still in Iran and were understood to be safe and well and their families had been informed, the statement added.
Foreign Office officials "immediately contacted the Iranian authorities in London and in Tehran on the evening of 25 November, both to seek clarification and to try and resolve the matter swiftly", Miliband said.
"Our ambassador in Tehran has raised the issue with the Iranian Foreign Ministry and we have discussed the matter with the Iranian embassy in London.
"I hope this issue will soon be resolved. We will remain in close touch with the Iranian authorities, as well as the families."
The Volvo 60 class yacht, called Kingdom of Bahrain and owned by the Sail Bahrain project launched by the Team Pindar sailing team, was due to have reached Dubai on November 26 to take part in a 360-mile Dubai-Muscat race, local media reported last week.
Along with the rest of the race fleet, it was to have passed through the shallows of the Gulf into the Indian Ocean before arriving in the Omani capital Muscat.
Tension has dogged relations between Britain and Iran in recent years over a range of issues from Tehran's nuclear program to Iranian allegations of British involvement in post-election violence in June this year.
Britain protested to Iran over a speech by Supreme Leader Ayatollah Ali Khamenei in the wake of the June protests, in which he called it "the most treacherous" of Iran's enemies.
In March 2007, relations between London and Tehran hit a low point after Iranian forces seized eight British Royal Navy sailors and seven marines in the mouth of the Shatt al-Arab waterway that separates Iran and Iraq.
They were freed unharmed the following month as a "gift" from President Mahmoud Ahmadinejad who scolded Britain for not being "brave enough" to admit they had made a mistake and strayed into Iranian waters.
Three Americans who crossed into Iran from northern Iraq in July this year are still detained and face spying charges. Their families say they were hiking and strayed across the border accidentally.
On Sunday, Miliband was among several world leaders to condemn Iran's announcement that it planned to build 10 new uranium enrichment plants in a major expansion of its atomic program. He accused Iran of choosing to "provoke and dissemble" rather than engage in talks. (Reporting by Avril Ormsby; Editing by Andrew Dobbie)
