Members of the Public and Commercial Services (PCS) union, including Border Force officials, will walk out on 15 March, with the impact of the action set to run into the early hours of 16 March.
The strike will impact international arrivals at all UK air and maritime ports, the Home Office warned, as well as those travelling to the UK from UK border controls in Calais, Dunkirk and Coquelles in northern France.
In a statement, the Home Office said: "If you are travelling into the UK during the proposed industrial action, be prepared for longer wait times at UK border control.
"Please be patient and respect officers who are working to keep our citizens safe and border secure, and supporting travellers during the strike action."
Passengers have been advised to use eGates if eligible and check with travel agents, tour operators and airlines before travelling.
Military personnel, civil servants and volunteers from across government are being trained to support Border Force at airports and ports across the UK during periods of industrial action.