Members of the Communication Workers Union will walk out on October 31, with more action in the run-up to Christmas not ruled out.
It will be the second strike in the row over job losses, the closure of the final salary pension scheme, and the closure of Crown post offices.
Three meetings have taken place at the conciliation service Acas but no meaningful progress was made.
Dave Ward, CWU general secretary, said: “The stakes have never been higher for the future of the Post Office, its workers and the communities they serve. The Post Office is at crisis point and the management and Government need to listen to the workforce.
“Staff and the public are seeing little more than a glorified closure programme from the Post Office and it cannot survive by simply cutting costs.
“We are calling for the Government as the owner of the Post Office to step in, halt the cuts and work with us to develop a proper strategy that will secure the future of the service.”