Sailors on board supply ship RFA Wave Knight tried in vain to catch the animal so the vessel could dock.
Crew reportedly used a cargo net in an attempt to snare the mum and baby she was carrying.
But before they could catch the monkey, the animal leapt off the Wave Knight and started swimming towards the shore.
It’s believed the green monkeys sneaked aboard Wave Knight in Bridgetown, Barbados.
The primates were seen dashing around the ship before then clambering onto the roof of the ship’s bridge.
The chase to catch the monkeys was sparked after officials at Grand Turk Island in the Atlantic said they would refuse to let the naval vessel dock while the animals were on board, citing ‘biosecurity reasons’ for the stance.
‘It all went wrong when the crew was trying to net her. It was really bad,’ a source told The Sun.
The Royal Navy said: ‘We take our responsibility to wildlife seriously and try to help.’
RFA Wave Knight is deployed as part of the UK’s Caribbean task group, working alongside the Portsmouth-based patrol ship HMS Medway, which is the UK’s permanent presence in the region.
The tanker’s main role is to provide support to British overseas territories in the event of a natural disaster, with peak hurricane season running from August to November.
This year the ship has delivered over 75 tonnes of aid to St Vincent following the volcanic eruption in April, helped scientists and island authorities prepare for another potential eruption, and supported the international relief effort in Haiti after last month’s devastating earthquake.
The task group also works alongside regional navies, authorities and police forces – especially the US Coast Guard – to tackle criminal activity across the Caribbean.
Last year Royal Navy ships and helicopters in the Caribbean – again working side-by-side with US authorities – seized cocaine worth nearly £400m.
In September the navy’s Caribbean task force seized almost £17m worth of cocaine less than 24 hours into the groups first drugs patrol of their deployment.