Nikkei 225 Index
Japan's Nikkei 225 index fell 4.8%, South Korea's Kospi lost 7.3%, and Australia's ASX shed 4.7%.
Earlier in the US, the Dow Jones stock index dropped 5.6%, despite US President Barack Obama trying to reassure investors.
A US recession would hurt Asia's export-led economies.
"You can't control it," Peter Esho, chief market analyst at City Index, told the BBC.
"You have the onset of fear in the market. There are a lot of things that don't make sense."
A number of issues have created the current market pessimism.
At the heart of the sell-off is the fear that ongoing debt problems in the US and Europe will slow economic growth and dent corporate profits.
On top of that, on Friday the US had its triple A credit rating cut by Standard and Poor's for the first time in history, adding to the sense of gloom surrounding the world's biggest economy.
"What's rocking the market is a growth scare," said Kathleen Gaffney of Loomis Sayles.
She said investors were concerned about "how Europe and the US are going to work their way out of a high debt burden" if the global economy slows.
With this in mind, other asset classes were also impacted on Tuesday. Crude oil prices continued to slide amid concerns that demand would wane in coming months.
Gold, meanwhile, hit a new record as investors looked for assets that are considered to be less risky. The Swiss franc also gained.
Analysts said that while economies in Asia had been growing robustly and the outlook for the region remained positive, a slowdown in the US and Europe could hurt growth significantly. Not least because the stock market slump may put off consumer and corporate spending.
"When you see such significant falls, Asia cannot distance itself completely," said City Index's Mr Esho.
Rajiv Biswas of IHS Global Insight told the BBC that investors were also worried that the cut in the US credit rating would force a serious reining in of bugetary spending.
"That will be a big drag on growth," he said.
Mr Biswas added that there was "little doubt" that a slowdown in the US and Europe would hurt growth and trade in Asia.
Analysts said that Asian economies may now have to revise their own economic projections as a result. On Monday, Singapore cut its growth forecast for this year to between 5-6%, down from 5-7%.
"The discussion now in Asia is to have a look at growth assumptions and perhaps even to revise numbers that could be a little too optimistic in light of what is happening the markets," said City Index's Mr Esho.
Investors have been dumping stocks across all industries in the US and Asia.
The S&P 500 index was down 6.7% in New York on Monday, the worst drop since December 2008, with every listed stock falling.
In points terms, the Dow ended down 635 to 10,810, its biggest one-day decline since October 2008, and the sixth largest on record. The Nasdaq index fell even further, losing 6.9%.
Earlier in the UK, the main FTSE 100 index lost 3.4%, or 178 points. It was the first time in the FTSE 100's 27-year history that it had fallen by more than 100 points for four sessions in a row.
Share indexes also fell heavily across Europe on Monday, with Germany's Dax ending down 5%, while France's Cac lost 4.7%.