FRANKFURT — The euro fell against the dollar Monday, and Asian stocks slipped, after Italian voters rejected changes to their country’s Constitution designed to speed government decision making and spur Italy’s stagnant economy.

The vote, and the political and financial turmoil it is likely to provoke, raised fears that Italy would be unable to muster the growth needed to deal with crushing government debt and a shaky banking system. The vote was another sign of popular resistance across Europe to changes that economists say are needed for the eurozone to overcome problems that have threatened its existence.

The political uncertainty caused by a “no” vote will postpone plans to rebuild the Italian banking system and help banks deal with deal with problem loans, which account for 18 percent of the total and are a serious drag on the economy.

The market interest rate, or yield, on Italian government bonds also rose, a sign that investors now consider the country to be a riskier place to put their money. Spanish and Portuguese yields also rose.

Initial market reaction to the vote was muted because investors had anticipated the result based on polls and had already adjusted their portfolios. Still, the euro slipped more than a cent against the dollar in early trading, and most Asian stock markets were slightly down. The Shanghai Composite index fell 1.1 percent, and the Nikkei 225 Index in Japan fell 0.9 percent.

The most immediate concern for investors is probably the Italian banking system. Prime Minister Matteo Renzi said he would resign, postponing if not derailing government plans to restructure Monte dei Paschi di Siena, Italy’s most troubled bank and a linchpin of the financial system.

“This is a critical point for restructuring of the Italian banking system,” said Ángel Talavera, senior eurozone economist at Oxford Economics in London. Rebuilding the banks is “critical for the economy,” he said before the vote.

Problems at Italian banks could spread across the eurozone. Large banks around the Continent continually lend money to one another, which allows problems at one institution to spread quickly. The extent of such exposure does not usually become clear until a big bank gets in trouble.

In the worst case, Italy could again be at the center of a crisis like the one that nearly destroyed the eurozone in 2011. The vote could set off a political chain reaction that would end with a government led by the populist Five Star Movement.

“The risk in Italy is that a Five Star party-led government is coming next, and it will move to pull Italy out of the E.U.,” Carl Weinberg, chief economist at High Frequency Economics in Valhalla, N.Y., said in a note to clients Monday. “That prospect undermines the creditworthiness proposition underlying Italian bonds.”

Italy’s national debt is equal to 136 percent of gross domestic product, second in Europe only to Greece. The government depends on investors willing to continue rolling over the debt at reasonable interest rates.

Investors have already been demanding a higher premium on Italian bonds. The market interest rate, or yield, on Italian 10-year government bonds has nearly doubled since August, to more than 2 percent. That is still far below the more than 7 percent reached in late 2011, during the darkest days of the eurozone financial crisis. But the increase is a sign that investors consider the bonds to be more risky.

If Italian bond yields continue to rise, investors could begin to doubt the government’s solvency.

The European Central Bank, which is scheduled to meet Thursday, is expected to extend its purchases of eurozone government bonds to hold down borrowing rates. But analysts say central bank measures cannot keep the currency bloc together indefinitely if its members are unwilling to take measures essential to growth.

There is danger of a vicious circle if the Italian economy sags. More businesses and consumers would have trouble paying their debts, and the number of problem loans could rise further. Bad loans are a dead weight on the Italian economy, because they prevent banks from providing credit needed for businesses to expand. And problems at Italian banks would become even more intractable.