The convicts pose a 'serious threat of the complete breakdown of law and order' on the islands, according to foreign minister Sir Alan Duncan.
Speaking to MPs in the Commons, Sir Alan said marines from RFA Mounts Bay were used to 'protect the Governor and everything else about law and order' after the storm hit on Friday.
He also revealed that more than 500,000 British nationals have been in the path of the hurricane, and nearly 1,000 British military personnel are now in the Caribbean to help with the relief effort.
The announcement came as Boris Johnson travelled to the Caribbean to visit the British overseas territories battered by Irma.
Mr Johnson, speaking while on a plane to the region, told the Press Association the military presence was 'really ratcheting up now'.
The hurricane was 'an unprecedented event, an unprecedented catastrophe' for the people in the part of the Caribbean which has been worst hit, he said.
'What they're seeing is an unprecedented UK response. But I want to stress it is not just for the short term, we are going to be there for the long term as well,' he added.
He rebuffed criticism of Britain's response, saying: 'We had RFA Mounts Bay in position in the region before the hurricane struck - it would have been totally absurd to bring troops in or bring heavy aircraft during the storm itself.'
He added that the number of troops would go up to 1,250 in the next few days.
So far, 20 tons of UK aid has arrived in the region - including 2,500 shelter kits and 2,300 solar lanterns.
The Foreign Secretary is expected to visit the British Virgin Islands and Anguilla, two of the worst-hit territories, where nine people were killed.
French President Emmanuel Macron is also visiting the region, and his trip to St Martin is expected to coincide with the arrival of a military ship carrying supplies.
Some Britons stranded on affected islands said they felt abandoned, while others claimed the Dutch and French governments - which also have Caribbean territories - were better prepared and quicker to respond.
Another Royal Navy ship, the HMS Ocean, is set to arrive in the Caribbean within days.
Irma was downgraded to a tropical storm on Monday, after inflicting record flooding and deadly devastation in Florida and on several Caribbean islands.
The weather system is continuing to weaken, and the National Hurricane Centre says Irma will likely have dissipated by Tuesday evening.
As a category five hurricane, the rare top end of the scale of hurricane intensity, the storm killed nearly 40 people in the Caribbean.