Around 1,500 members will join the one day strike, with normal services to resume on Tuesday, July 12.
The union has said the offer was “woefully inadequate” and well below the rate of inflation, which hit 9.1 percent in June.
Andy Furey, an assistant secretary of the CWU, said: “No worker wants to be in this situation but Post Office bosses can’t be surprised that callous decisions are challenged by our members.
“This dispute is about dignity and respect for hard-working employees, essential public servants who, as key workers, provided unprecedented customer service during the pandemic.”