The euro zone took the unprecedented step of taking a bite out of depositors' bank accounts to help pay for its bailout of Cyprus, a high-risk decision that could erode savers' confidence across the currency bloc and add to popular anger over its handling of the financial crisis.

The decision to raise €5.8 billion ($7.6 billion) from taxes on depositors—including individuals with small amounts in their accounts—risks a political backlash for the newly elected center-right government on the Mediterranean island and a wider political fallout for the euro-zone leaders who are guiding the bloc's crisis strategy.

Asian shares and the euro fell sharply in early trading Monday as markets reacted to the bailout. Japan shares dropped 2.1%, Hong Kong fell 2.0% and Australia fell 1.4%. "The feeling is that the euro crisis could be back and that you could see full-on contagion," said Shane Oliver, head of investment strategy and chief economist at Amp Capital in Sydney. "But I suspect that we are going to hear reassurances from other countries."

A tax on depositors—6.75% on deposits up to €100,000, and 9.9% above that level—was the only way out for the bloc's finance ministers after Germany, the euro zone's biggest economy, and the International Monetary Fund insisted that financial aid to Cyprus should be limited to €10 billion.

With the money due to have been withdrawn electronically from bank accounts over the weekend, politicians in Nicosia were discussing how they might adjust the levy to make it appear fairer. Monday is a public holiday on the island, when banks are closed, but European officials said contingency plans were being put in place to calm any turmoil in the country's financial system when the banks eventually reopened.