Unite said the 24-hour walkout on December 3 will disrupt overseas Christmas mail and parcels.
Around 720 managers will take action, the third 24-hour strike in a long-running pensions’ dispute.
The managers will be joining a strike by members of the Communication Workers Union, which is in dispute over jobs and the franchising of Crown Post Offices as well as the closure of a final salary pension scheme.
Unite union officer Brian Scott said: “We believe that Saturday is the day when most people will be despatching their cards and parcels to their relatives and friends abroad.
“We are taking this action because the management refuses to talk in a constructive manner about the pension scheme which is currently in surplus to more than £143 million.
“This is the retirement income of our members which is at stake and we are not going to stand idly by and let them lose thousands of pounds when they retire.
“More generally, it appears that it is only the unions that care about the future viability of the Post Office and the services it provides for communities across the UK.
“The management seems to have abdicated its responsibility and, as the Government ultimately owns the Post Office, we call, once again, for Business Minister Margot James to order an investigation into the Post Office’s future and what we consider is a catalogue of managerial incompetence.”
Mark Davies, communications and corporate affairs director at the Post Office, said: “We are extremely sorry that the unions are attempting to disrupt services for people sending parcels and cards to loved ones in the run-up to Christmas.
“However, we would like to reassure our customers that, if a strike goes ahead on December 3, it will impact less than 300 of our 11,600 branches.
“It will be business as usual in 97% of our network with almost all of our network operating to its usual Saturday schedule.”