The deployment follows a visit by a British junior foreign minister to Guyana earlier this month, intended to offer the UK's support for the country, an ally and former British colony.
Guyana and Venezuela agreed earlier this month to avoid any use of force and not to escalate tensions in the long-running dispute.
Venezuelan Defense Minister Vladimir Padrino said in a social media post on Sunday that his country would remain "on alert following provocations that put at risk the peace and stability of the Caribbean and our America."
The 160,000-square-km (62,000-square-mile) Essequibo region is generally recognised as part of Guyana, but in recent years Venezuela has revived its claim to the territory and to offshore areas after major oil and gas discoveries.
Britain will deploy the Royal Navy patrol vessel HMS Trent, the ministry of defence said in a statement, without referring to Venezuela or the border dispute.
"HMS Trent will visit regional ally and Commonwealth partner Guyana later this month as part of a series of engagements in the region during her Atlantic Patrol Task deployment," a spokesperson said.
(Reporting by Sachin Ravikumar in LondonAdditional reporting by Vivian Sequera in CaracasEditing by Mark Potter and Matthew Lewis)
