The men were seized at 1030 local time when they boarded a boat in the Gulf, off the coast of Iraq, which they suspected was smuggling cars
The Royal Navy said it was doing everything it could to secure the release of the sailors and marines who are based on HMS Cornwall.
They were said to be carrying out a routine patrol in Iraqi waters.
The Ministry of Defence said: "The group boarding party had completed a successful inspection of a merchant ship when they and their two boats were surrounded and escorted by Iranian vessels into Iranian territorial waters.
"We are urgently pursuing this matter with the Iranian authorities at the highest level.
"The British government is demanding the immediate and safe return of our people and equipment."
It is understood the men being held are safe and well.
Foreign Secretary Margaret Beckett has summoned the Iranian ambassador in London to the Foreign and Commonwealth Office, in an attempt to get the sailors and marines released as quickly as possible.
In a statement, leader of the Liberal Democrats, Sir Menzies Campbell, also called for their immediate release.
"Whatever the rights and wrongs of military action, British forces in Iraq are now there with the authority of a UN security council resolution... and the Iranian government should be left in no doubt of the serious implications of their action," he said.
In 2004, Iran detained eight British servicemen for three days after they allegedly strayed over the maritime border.
The UK claimed the men were "forcibly escorted" into Iranian territorial waters.
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