By Matthew Dalton and Marcus Walker 

The threat of broad sanctions by the West against Russia is starting to sever the economic ties that have bound them closer since the end of the Cold War.

Western governments hope the latest sanctions on Moscow, including new European Union measures agreed upon Tuesday, will hit the pressure points of Russia's wobbly economy, with only minimal cost to the EU or the U.S.

The EU's sanctions for the first time target sectors of Russia's economy, including its state-controlled banks and its oil industry. The moves remain tightly focused because the EU wants to give President Vladimir Putin a chance to stop his alleged support of rebel groups in eastern Ukraine.

But the accumulation of measures is likely to have an effect that goes beyond the specific ones adopted by Western officials. They send a strong message to companies and investors that much of the Russian economy is out of bounds, analysts and economists say.

"Unless you've got a very high tolerance for risk, no one is going into Russia," said Neil Dooley, an attorney at Steptoe & Johnson in London who advises companies and investors on Russian sanctions issues.

The country's economy is already struggling: A slow recovery from the global financial crisis has already petered out. The turmoil in Ukraine appears to have slammed Russia's growth prospects, leaving it on the brink of renewed recession.

The International Monetary Fund last week cut its growth forecast for the Russian economy this year to 0.2%. A year ago the fund forecast Russian growth at 3.8% in 2014.

The West's fresh sanctions are likely to heap new pain on the Russian economy. The EU is expected to limit access by Russian financial institutions to European capital markets, ban new arms deals and restrict exports of militarily-sensitive goods and equipment used in unconventional oil production. The U.S. is planning similar sanctions, officials said this week.

Those measures go well beyond previous sanctions against Russia that targeted officials, a few companies and some well-connected oligarchs.

"Russia's already weak growth could become clearly negative," said Adam Slater, senior economist at U.K.-based consultancy Oxford Economics.

The chilling effect of the measures is likely to go beyond their direct scope, which still allows most trade and investment ties with Russia to continue.

"They signal that Russia is a location where investment is not really approved, or is risky because sanctions might be extended further," Mr. Slater said.

The potential legal risk presented by dealing with Russian companies while sanctions are in place is already proving to be a formidable obstacle, particularly for big companies and investors, sanctions lawyers say. Though the Western sanctions aren't supposed to affect existing contracts, European companies are going to be wary of delivering goods and services under their terms.

"Is it retroactive when the obligation is to supply in the future?" Mr. Dooley said. "I think many would construe that as a breach of sanctions."

Russia is already suffering from significant capital flight, as foreign investors and some Russians pull money out amid concern over the economic outlook. Russian banks and companies have so far filled the gap by borrowing from international markets or from the Russian central bank.

The EU measures are expected to target Russia's largest financial institutions, including Sberbank and VTB Group, diplomats say. EU investors will be forbidden from buying most debt and equity newly issued by financial institutions that are majority-owned by the Russian government, according to draft documents seen by The Wall Street Journal.

The measures would create headaches for Russian banks, which have large debts that are denominated in foreign currencies. Citibank analysts said in a note this week that VTB appears to be more vulnerable than other Russian banks, given its relatively high reliance on bond markets for funding.

The restrictions could push banks to search for funding either from the Russian government budget or the Central Bank of Russia, economists say. That could present Russia with the unattractive option of drawing down its large foreign currency reserves, worth roughly $500 billion, or allowing a sharp fall in the ruble that would raise inflationary pressure.

Russia's main economic role in Europe--as a supplier of natural gas--is so important to both sides that it is likely to continue, unless vital pipeline links fall victim to an escalation of the war in Ukraine.

If fear of a disruption of supplies pushes oil and gas prices higher, that could also hurt EU industries, although European households don't need to heat much right now.

The still-narrow measures in the EU's latest moves could affect some industries, but probably won't do measurable harm to the overall European economy, economists said.

Even in Germany, where business associations continue to lobby for restraint in EU sanctions, only 3.3% of exports go to Russia, and most German export sectors enjoy a well-diversified portfolio of global customers. Growth in China, the U.S. and France will continue to matter more for Europe's biggest economy.

The economic fallout in EU countries depends on what happens next. If Moscow doesn't change its policies in Ukraine and EU sanctions get progressively tougher, then the disruption of economic and financial ties could eventually be felt widely in Europe, analysts said.

Mr. Putin might eventually see the virtue of defaulting on the external debt of Russia's state-owned companies, said Mujtaba Rahman, an analyst at Eurasia Group in London.

"The Russian response could then be to engineer external default as a way to hurt European markets and the U.S.," Mr. Rahman said.

Financial links could be the most troublesome to disentangle, said Robert Kahn, a senior fellow at the Council on Foreign Relations in Washington. A broader ban on financial transactions could cause major dislocations in Europe's financial system, with unpredictable consequences for markets, he said.

According to the figures from the Bank for International Settlement, French banks were owed $50.3 billion by Russian borrowers at the end of March, Italian banks $27.2 billion, German banks $23.1 billion and U.K. banks $16.8 billion.

"We're not there yet. What the EU is trying to put in place is intended more as a slow squeeze than a disruptive break," he said.

But there is now "an inexorable momentum" for more sanctions over time, because of Russia's reluctance to back down in Ukraine and the EU's mounting impatience with Moscow, Mr. Kahn said. "This is not the end of the story."

Lukas I Alpert contributed to this article.

Write to Matthew Dalton at Matthew.Dalton@wsj.com and Marcus Walker at marcus.walker@wsj.com