Benchmarks in Tokyo, Hong Kong and Sydney closed down and London, Frankfurt and other European indexes were trading lower. Wall Street futures was also expected to dip on the open.
Traders shifted money into bonds and gold, a traditional safe haven.
Bond markets are "sounding a warning on global growth" as virus fears spread to South Korea, Singapore and other economies, DBS analysts said in a report.
Markets had been gaining on hopes the outbreak that began in central China might be under control following government controls that shut down much of the world's second-largest economy. Sentiment was buoyed by stronger-than-expected U.S. economic data and rate cuts by China and other Asian central banks to blunt the economic impact.
But investors were jarred by South Korea's report of 52 new cases of the coronavirus, raising its total to 156, most of them since Wednesday. That renewed concern the infection is spreading in South Korea, Singapore and other Asian economies. New cases were also recorded further afield, from Italy to Iran.
In Europe, the FTSE 100 in London sank 0.2% to 7,422 and Frankfurt's DAX lost 0.1% to 13,656. France's CAC 40 tumbled 0.1% to 6,054.
Losses were trimmed after a survey showed that business activity in the eurozone improved in February despite the disruption from the virus outbreak. In particular, the slump in Germany's manufacturing sector seemed to ease, though the ultimate impact of the outbreak on companies remains still unclear.
On Wall Street, the futures for the benchmark S&P 500 index and for the Dow Jones Industrial Average both lost 0.3%.
In Asia, Tokyo's Nikkei 225 declined 0.4% to 23,386.74 and Hong Kong's Hang Seng sank 1.1% to 27,308.81. In Seoul, the Kospi lost 1.5% to 2,162.84.
The Shanghai Composite Index bucked the regional trend, climbing 0.3% to 3,039.67.
The S&P-ASX 200 in Sydney lost 0.3% to 7,139.00. New Zealand advanced while Southeast Asian markets declined.
A measure of Japan's manufacturing activity tumbled to an eight-year low and a companion gauge of service industries dropped even more sharply.
The decline "underlines that the coronavirus has started to weaken activity," Marcel Thieliant of Capital Economics said in a report.
The airline industry association estimated that the virus outbreak will cost the sector some $29 billion in revenue.
To contain the disease, China starting in late January cut off most access to Wuhan, the central city where the first cases occurred, and extended the Lunar New Year holiday to keep factories and offices closed and workers at home.
Some Chinese factories and other businesses are reopening but restrictions that in some areas allow only one member of a household out each day still are in place. Forecasters say auto manufacturing and other industries won't return to normal until at least mid-March.
A rise in new cases in Beijing, the capital, "raises alarm" because it suggests major Chinese cities "may be under pressure to contain the virus amidst returning workers" as companies reopen, Mizuho Bank said in a report.
In energy markets, the benchmark U.S. crude contract lost $1.00 to $52.88 per barrel in electronic trading on the New York Mercantile Exchange. The contract rose 49 cents on Thursday. Brent crude oil, the international standard, lost $1.13 to $58.18 per barrel in London. It rose 19 cents the previous session.
The dollar declined to 111.87 yen from Thursday's 112.09 yen. The euro rose to $1.0807 from $1.0790.