It was especially dire in Shanghai: China's benchmark index plummeted 7.2 percent to its lowest point in six months on concerns that a recession in the U.S. would mean less demand for Chinese-made products.
Chinese businesses are worried that they will be selling fewer exports, the engine behind its growing economy, says CBS News correspondent Barry Peterson.
European markets also fell in early trading, and U.S. stock index futures were down, suggesting that Wall Street was poised to drop again when markets opened.
Investors around the world have been jittery for weeks about a U.S. slump, which would likely weaken demand for exports and drag on global growth. There is also concern about a worldwide credit crunch triggered by rising defaults in risky U.S. mortgages, which has led to mountains of bad assets at major American and European banks.
"There's a lot of uncertainty out there: uncertainty over the U.S. economy, uncertainty over China's economy," said Rob Hart, an analyst with Morgan Stanley in Hong Kong.
"People are also worried about contagion in Europe. If the U.S slows down, will it trigger a slowdown in Europe?" he said.
In Europe, the U.K.'s FTSE dipped 1 percent to 5,807.9 in morning trading. Germany's DAX slipped 1.2 percent while France's declined 1.7 percent.
In Asia, Tokyo's benchmark Nikkei 225 index fell nearly 4 percent to close at 13,087.91, erasing its jump on Friday, while Hong Kong's Hang Seng index sank 4.3 percent.
Declines were more modest in India, where the Sensex index - which plunged 4 percent in the first 10 minutes of trading - was down just 1.1 percent in late afternoon trading.
The sharpest declines came in China, where the Shanghai Composite index plunged 342.39 points to 4,419.29 amid worries about weaker demand from American consumers. Concerns over the potential impact of a prolonged bout of severe winter weather also took a toll.
"Investors, especially institutional investors, are very cautious," said Chen Huiqin, an analyst at Nanjing-based Huatai Securities. She said investors were waiting for possible "market rescuing" signals from the Chinese government.
"That could have a strong impact on the market," Chen said.
Global markets dropped sharply early last week on worries about slower U.S. growth. They rebounded after a hefty three-quarters cut in U.S. interest rates by the Federal Reserve last Tuesday, as well as on news of a stimulus package that Washington is hammering out.
But investors in Asia and Europe dumped shares again Monday after Wall Street sank Friday, when the Dow Jones industrials slid 1.38 percent and the technology-heavy Nasdaq composite index declined 1.47 percent.
Some traders said Asian markets dropped on concern that the Fed may not slash interest rates again - or as much as expected - when its policy planners meet Tuesday and Wednesday.
"The possibility for a 50 basis points cut is looking less likely," said Castor Pang, a strategist at Sun Hung Kai Financial in Hong Kong, pointing to future prices in New York.
Dow futures were down 80 points, or 0.65 percent, to 12,156, while Nasdaq futures were down 16.5 points, or 0.92 percent, to 1,777.
Japan's economy - heavily dependent on exports - may already be contracting, said Tetsufumi Yamakawa, chief economist at Goldman Sachs Japan.
He pointed out that five of the 11 components of Japan's business condition diffusion index have already hit highs and begun to deteriorate. Declines in six of the 11 components often indicates a recession is coming.
"A recession, which was nothing more than a risk scenario six months ago, is now turning into our main scenario," Yamakawa said in a report released Friday.
Japanese traders also were cautious ahead of a slew of corporate quarterly earnings this week, including Honda Motor Co. on Wednesday and Sony Corp. on Thursday.