The result of the ballot, which closed on Tuesday, means deliveries may be affected across the EH (Edinburgh and Lothians),TD (Borders), FK (Stirling and central areas) and KY (Glenrothes and Fife) postcodes.
The dispute centres round the sacking of postman Dave Mitchell, 57, dismissed in December 2014 after a number of “test” items went missing.
Mr Mitchell, from Chance Inn, near Cupar, maintained he was innocent and took his case to an employment tribunal. Judge Ian McFatridge twice ordered his reinstatement but Royal Mail refused to comply.
Ray Ellis, CWU assistant secretary, said: “We have got a ‘yes’ vote from Dave Mitchell’s colleagues in the branch but we now seeking urgent talks with Royal Mail to resolve the issue.”.
It is understood that just over 52 per cent of the CWU membership voted to strike.
The union has 28 days to set a strike date and must give Royal Mail seven days’ notice.
Mr Mitchell’s colleagues held two 24-hour strike days, the first a week before Christmas and the second in January 2016.
There have also been a number of “silent” protests outside the Cupar delivery attended by Mr Mitchell’s former customers, family and friends.
Stephen Gethins SNP MP for North East Fife, urged Royal Mail to reinstate him saying “this should not be that difficult to resolve”.
“Dave has a huge amount of support from local communities in north-east Fife who have showed tremendous support for him during this difficult period. It is clear that he also enjoys support from those he worked with in Cupar and elsewhere in Scotland.
“This has always been a simple case of fairness and Royal Mail respecting the decisions of the employment tribunal. The ball is very firmly in Royal Mail’s court and I hope that they will look at reinstating my constituent and respecting the decisions of the tribunal. This should not be that difficult to resolve.”
A Royal Mail spokeswoman said: “Royal Mail is very disappointed CWU members across four postcodes in the east of Scotland have voted for industrial action over an employment tribunal case. Any action or threat of action is damaging to our business.
“In this case, there was sufficient evidence for us to dismiss Mr Mitchell. Four out of five test pieces of mail for Mr Mitchell’s delivery frame went missing on three separate occasions. All other test items in this office for other employees were delivered correctly.
“We are continuing to talk to our people and unions about this matter. We have robust contingency plans in place to ensure we continue to deliver a high quality service to affected postcode areas.”