Members of the Communication Workers Union (CWU) backed action by 9-1 in protest at plans to franchise or close over 70 Crown offices - the larger branches usually sited on high streets.
Union members have staged a series of strikes since Easter, but the latest ballot result means the union can organise different forms of industrial action.
The CWU raised the prospect of a ban on the sale of insurance, credit cards and other banking products.
Dave Ward, CWU deputy general secretary, said: "This ballot result sends another strong message to Post Office management that their staff completely disagree with their business plan and will not be trampled on. A sales ban will hit an integral part of the Post Office's business plan and hopefully focus minds to resolve this dispute.
"Staff are feeling alienated from the company's controversial business plan which is overly reliant on cuts, closures and aggressive sales targets. We are concerned that sales targets are over-ambitious and could lead to hard-sell tactics which would be at odds with the Post Office brand.
Turnout in the ballot was 58%.
A Post Office statement said: ""We are very disappointed that the CWU has chosen to take this step.
"Growing our financial services business is a vital part of transforming the Crown network and meeting our objective of getting the Crowns to break even by March 2015. We would like to reassure customers that they will be able to continue to access these services at Crown branches.
"The action the CWU is suggesting is for its members working in around 370 Crown branches across the UK to stop proactively introducing these services to customers. This can only cost its members money and disadvantage our customers.
"We hope our people will recognise that taking this course of action can only place further pressure on the Crown network which is currently losing £37 million a year.
"We must continue with our plans to turn around the Crown network to ensure we keep these branches on high streets and in city centres across the UK. We remain open to discussions with the CWU on pay options which do not add to the current loss of public money."