Members of the Communication Workers Union (CWU) will walk out on July 14.
Employed in supply chain and admin jobs, the workers deliver essential supplies, valuables and cash to thousands of sub-post offices, process finances and work in administration.
The dispute is in opposition to a pay offer from the Post Office which the union said was worth three percent for 2022/23, alongside a one-off lump sum payment of £500, and no pay increase for the 2021-22 financial year.
The union said the proposals are far beneath the RPI inflation rate of 11.7 percent.
CWU Assistant Secretary Andy Furey said: “The blame for this disruption lies entirely with the senior Post Office leadership, who have repeatedly failed – and wilfully refused – to set out a sensible and fair pay agreement.
“Everyone knows that the only solution is a fair pay rise that properly rewards members for their extraordinary efforts in serving the public and delivering a profitable Post Office, while also taking account of the extreme cost of living.
“There most certainly is money available, but management do not want to give workers their fair share.
“Our message to the employer today is: don’t waste our members’ time by misleading statements.
“Stop the spin and get serious about pay. Until you do this, the strikes will continue.”
A Post Office spokesperson said: “We have received notice that the CWU has called a strike involving supply chain colleagues.
“We will have a range of contingency measures in place to minimise any possible disruption to the Post Office network on that day.”
The CWU also announced that Crown Post Office workers will be striking on July 11 in a separate pay dispute.