Futures tied to the Dow Jones Industrial Average dropped almost 5%, signaling that the gauge of U.S. blue-chip stocks will start the week about 1,000 points lower. Trading limits prevent futures from losing more than about 5% in out-of-hours trading.

Investors shifted funds into the shelter of U.S. government bonds, reflecting continued anxiety about global growth prospects. The yield on the benchmark 10-year U.S. Treasury note dropped to 0.794%, from 0.946% at Friday’s close. The Fed took several steps last week to calm the Treasury market, which is the most liquid and actively traded bond market in the world, as outsize swings in yields and other safe-haven assets added to the global turbulence.

The Fed’s second emergency rate cut this month—disclosed Sunday evening—hasn’t been well-received since it appeared to investors to be a “sign of desperation,” said Terence Wong, chief executive of Azure Capital, a Singapore-based fund management firm.

“It’s basically using up all their ammunition within a three-week span,” said Mr. Wong. “There’s nothing left. They can’t use monetary loosening as part of their arsenal anymore.”

In addition to slashing borrowing costs, the Fed said it would buy $700 billion in Treasurys and mortgage-backed securities, cut the rate charged to banks for short-term emergency loans from its discount window and activate swap lines with five other central banks.

The pan-continental Stoxx Europe 600 declined 7.8%. Equity indexes in Hong Kong, Shanghai, South Korea and Japan all closed lower, falling between 2.5% and 4%.

“Investors are continuing the digest of the severity of the downturn that we’re experiencing in real time across the world,’’ said Rick Lacaille, chief investment officer at State Street Global Advisors. “It’s hard to process how temporary that shortfall is going to be.’’

Projections like Goldman Sachs Group’s forecast of a 5% drop in U.S. gross domestic product in the second quarter is weighing on market sentiment, with investors questioning whether the fallout from the outbreak will continue into 2021, Mr. Lacaille said.

The reaction in U.S. markets showed investors were already looking past the Fed and waiting for the federal government to act with bigger stimulus measures, said Joseph Brusuelas, chief economist at RSM U.S.

“Until they signal that they understand the magnitude of the coming demand shock, markets will continue to sell off and be subject to significant volatility,” Mr. Brusuelas said.

Fed Chairman

Jerome Powell told reporters that plunging oil prices were a factor in the Fed’s decision. Brent crude, the global gauge of crude prices, fell 7.6% to $31.27 a barrel, leaving the benchmark down in value by about half since the start of the year.

Chinese data showing the scale of the country’s virus-induced slowdown also fed a regional selloff. Economic statistics for January and February showed Chinese retail sales, investment in fixed assets and industrial output all fell sharply, and more than economists expected. Industrial output was 13.5% lower year-over-year.

In Australia, whose economy is heavily reliant on Chinese demand, the equity benchmark S&P/ASX 200 index fell a record 9.7%, to end the day some 30% below its highest close less than a month ago.

The figures showed the economic costs of an effective virus-containment strategy, according to Jim McCafferty, joint head of Asia-Pacific equity research at Nomura in Hong Kong.

“It is sending a frightening signal to the other economies. We will see a similar impact on global GDP numbers,” Mr. McCafferty said, as infection control takes priority over growth targets. In turn, corporate earnings and growth estimates will start to fall, he projected.

Japan’s Nikkei 225 index closed 2.5% lower on Monday, even after the Bank of Japan rolled out measures to blunt the impact of the novel coronavirus, including doubling its purchases of exchange-traded equity funds, and said it wouldn’t hesitate to take more action if needed.

Japanese Prime Minister Shinzo Abe said that the Group of Seven leaders would hold an extraordinary videoconference at 10 a.m. EST to coordinate their response to the coronavirus outbreak.

The WSJ Dollar Index, which tracks the dollar against a basket of 16 others, fell 0.2%.