The Communication Workers Union said the walkout would start on Monday 19 December and include Christmas Eve.
It will involve thousands of workers from the Crown Post Offices.
The Post Office said despite the walkout it would be "business as usual" with "at least" 97% of its 11,600 branches not involved.
Crown Post Offices are the larger branches that are usually located in High Streets.
In April 2016, the Post Office announced plans to transfer up to 61 branches into WH Smith stores over the following year.
It said the move was part of a 10-year plan to cut costs and save cash, and would act as a way of "safeguarding the future of the network."
"Our members want the Post Office management to pause its closure and privatisation programme, hold off on its planned pensions changes, and commit to sitting down with us and with the other key stakeholders of this Great British institution and, together, construct a lasting vision," said CWU assistant secretary Andy Furey.
The Post Office said it was "extremely disappointed" by the CWU's action.
"Just today, we agreed with the CWU that we would resume talks, which have been ongoing throughout the summer, on Wednesday," added Kevin Gilliland, the Post Office's network and sales director.
Post Office workers will stage five days of strikes from Monday in a continuing dispute over jobs, pensions and branch closures, their union says.