However the region's large foreign reserves and current-account surpluses will cushion it from the impact of another global financial crisis, while the bank said China could pick up some of the slack from the West.
In its twice-yearly report the Washington-based bank said developing East Asia see growth of 8.2 per cent this year and 7.8 per cent in 2012, down from 9.7 per cent in 2010.
"Lower growth in Europe in the course of fiscal austerity and the banks? needs to increase capital coverage would affect East Asia," said Bert Hofman, the bank's chief economist for the East Asia and Pacific region.
"Less credit from European banks can also affect capital flows to East Asia, but high reserves and current account surpluses protect most countries in the region against the impact of possible renewed financial stress."
According to the bank, the region -- which includes China, Indonesia, Malaysia, the Philippines, Thailand, Vietnam and Cambodia -- had foreign reserves, excluding gold, totalling $4.9 trillion as of September.
China alone has foreign reserves of $3.2 trillion.
The region's export-led economies have already been affected by the ongoing turmoil in the West with its industrial sectors, especially electronics, facing weaker demand, the World Bank said.
It added that flooding in several countries, including Thailand, contributed to the expected slowdown as companies in the region were forced to stop production due to broken supply lines and parts shortages.
With the US economy struggling and Europe grappling with a crippling debt crisis, China has emerged as a major export market that would be able to fill in some for the gaps in demand, the World Bank said.
The Chinese economy is still expected to expand at a solid 9.1 per cent this year despite Beijing's efforts to rein in inflation -- including raising interest rates -- with growth expected at 8.4 per cent next year, it said.
"China?s growing consumer goods market represents a potentially significant new opportunity for East Asian exporters, if it continues to expand from its low base of just two per cent of the world consumer goods market," it said.
China's share of global imports has grown steadily and it now buys as much as the European Union, the bank said.
For the short term, the main challenge for East Asia is how to strike a balance between stimulating growth and fighting the effects of the global uncertainty, the bank said.
The region's policymakers "are likely to hold off further policy tightening and stand ready to act should negative shocks to growth occur or in the unlikely event of a disorderly resolution of the eurozone debt problem," it added.
While fiscal positions are not as strong before the 2008 meltdown, most middle income countries in the region still have room for stimulus packages should it become necessary, the bank said.
For the medium to long term, however, East Asian policymakers must implement further reforms that will boost domestic demand and productivity.
"Higher investments in infrastructure, education and social security systems can help countries increase productivity and move toward higher value added production," said senior economist Ekaterina Vostroknutova, the report's lead author.
"Any possible stimulus programs should be fiscally sustainable, well-targetted and directed at promoting the structural transformation needed for stronger, domestically driven growth."
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