The strike - planned for 15 September and organised by the Communication Workers Union (CWU) - comes after the Post Office announced it would be closing its pension scheme.
Eighty-three per cent of CWU members voted for the walk-out.
Dave Ward, general secretary of the CWU, said: "The Post Office is relentlessly pursuing a programme of cuts that will mean a further 2,000 job losses, staff being left tens of thousands of pounds worse off in retirement and the privatisation of its flagship branches.
"We are making a simple demand. The government needs to pause the cuts, convene a summit of key stakeholders in the industry and work out a strategy that gives employees and the public confidence that the Post Office has a future."
CWU deputy general secretary Terry Pullinger said the Post Office's proposal to close the pension scheme had "no justification"; he said the surplus of the scheme is £130m, making it the best-funded scheme in the country.
"In closing it down the Post Office is stealing the money our members have built up over many years of service and backtracking on its promises to keep the scheme open," Pullinger said.
Kevin Gilliland, Post Office’s Network and Sales Director, said: "We can reassure our customers that 97 per cent of our 11,600 branches will not be involved in any action that goes ahead. We will also work hard to minimise any disruption to customers in our 300 Crown branches should they be affected by strike action.
"All of our proposals are taken forward with the utmost care for the people they affect and we’re proud of our track record in supporting people through difficult changes.
"The business’s financial position is improving but we remain loss making. Based on the advice of our Actuary, the fund’s surplus, which is currently being used to help subsidise the cost of the DB Plan, will run out in 2017.
"Once this happens, the costs to the business of meeting existing commitments will significantly increase, and this is not sustainable. We therefore need to close the DB Plan to future accrual when the surplus runs out, because it is crucial that we safeguard the benefits that members have already built up."