The Public and Commercial Services union is balloting members on action it warns could "potentially cause long queues at the UK’s largest airport".
The ballot opened at the weekend and will run until midday on 22 March; the earliest members could walk out in the event of a successful ballot would be on Friday 5 April. The Easter holidays run from Friday 29 March to Friday 12 April.
According to the union, Border Force is seeking to impose a new team working fixed roster, as well as amending legacy terms and conditions and flexible working arrangements.
PCS general secretary Fran Heathcote described the proposals as "an appalling way to treat long-serving, dedicated staff".
Heathrow said the dispute was a matter for the Home Office.
