The 28-nation bloc may now have to settle for a smaller group of countries agreeing on closer cooperation, in another sign of a divided, two-speed Europe.
Plans for a European prosecutor first emerged in 2009 to combat fraud that costs the bloc nearly 900 million euros a year.
But they have met resistance from some states who fear a loss of sovereignty as the proposed office would have powers to operate directly in member states.
The European Council said it "registered the absence of unanimity in support of the proposal for a regulation creating a European Public Prosecutor's office."
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"If this does not prove possible, enhanced cooperation can be considered," it added, meaning the group could push ahead with the prosecutor plans on their own.
The plan for a common prosecutor was designed to target fraud that has helped fuel populist anti-EU sentiment in Britain and other countries.
Seventeen countries including powerful Germany and France are willing to cooperate, while 11 including Britain and the Netherlands are not, according to the European Commission.
European Commission head Jean-Claude Juncker has said Britain's shock decision to leave the EU showed it could be time to develop a two-speed Europe, divided between countries that want more integration and those that want less.
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