The FTSE 100 Index, which has been trading at a five-year high above 6500 in recent days, slumped 100 points or 1.5%, while Japan's Nikkei ended the session more than 2.5% lower. Banks were among the biggest fallers in London.
Traders are worried that the precedent set by the planned move could spark an exodus of capital from other fragile European economies and jeopardise the region's recent tentative recovery.
Unlike the previous rescues for Greece, Portugal, Ireland, and Spanish banks, the proposed Cypriot bailout is the first one that dips into people's savings to finance a bailout.
In exchange for 10 billion euros (£8.6 billion) in rescue money, there will be a one-time tax of 6.75% on all bank deposits under 100,000 euros (£86,490) and 9.9% over that amount.
The bailout package, which has still to be finalised, involves the International Monetary Fund, European Central Bank and European Union.
Michael Hewson, senior analyst at CMC Markets, said: "If European policymakers were looking for a way to undermine the public trust that underpins the foundation of any banking system they could not have done a better job.
"Not only is it in complete contravention of the deposit insurance rules agreed by all EU countries in October 2008, and an absolute PR disaster, but it opens up a Pandora's box of all possibilities with respect to precedent and future measures in other EU countries that find themselves having to ask for help in the future."
On Friday, the Dow Jones Industrial Average ended a 10-day winning streak, its longest in nearly 17 years.
Cypriot banks got into trouble after losing some 4.5 billion euros (£3.8bn) on their Greek government bond holdings after eurozone leaders decided to write down Greece's debt last year.
President Nicos Anastasiades has urged MPs to approve the tax, saying it is essential to save the country from bankruptcy.
Mr Anastasiades, who assumed the Cypriot presidency on March 1, had rejected any idea of going after deposits to help pay for a bailout during the campaign and after his election.
He said: "The solution that we have reached is certainly not the one we wanted, but it is the least painful under the circumstances because above all it leaves the management of our economy in our own hands."
He said the tax would only be as much as the interest collected on deposits over two years and stressed that it would only happen once because it would ensure the bailout would not push the country's debt to unsustainable levels.
Savers would be compensated with bank shares and all depositors who opt to keep their money in Cypriot banks for at least two years would receive government bonds with a value equal to their losses, he added.
The bonds will be backed up by future revenue generated from the country's new-found offshore gas deposits. Pension and provident funds would remain untouched and there would not be any need for further salary and pension cuts or an earlier demand by creditors for a financial transaction tax, which would have damaged Cyprus' financial services-driven economy.
Cypriot MPs have already approved a raft of cuts to government workers' salaries and pensions as well as tax increases under a preliminary bailout deal.
The president said if he had not accepted the tax on bank deposits, the European Central Bank would have stopped providing emergency funds to the country's top two lenders which would have led to the collapse of the banking system, the bankruptcy of thousands of small businesses, job losses, and ultimately the country's exit from the euro.
Cyprus' parliament is due to hold an emergency session to discuss the bailout today, which has angered the public. A spokesman for one of the coalition partners, the Democratic Party, said it wanted assurances the deal would solve the problems facing Cyprus before it voted in favour.
Reports have suggested that eurozone leaders, particularly in Germany, insisted on the levy because of the large amount of Russian capital kept in Cypriot banks, amid fears of money-laundering.
The levy itself will not take effect until Tuesday, following a public holiday, but action was taken to control electronic money transfers over the weekend.