Regional growth is forecast to slow from 6.5 per cent in 2015 to 6.3 per cent this year and 6.2 per cent in 2017 and 2018, the bank said in its latest outlook.
However, Southeast Asian economies led by Vietnam and the Philippines are still expected to see healthy expansion, with both forecast to see growth rates of more than 6.0 per cent, it said.
The bank said the regional outlook reflected China's gradual shift to slower, more sustainable growth, expected at 6.7 per cent this year and 6.5 per cent in 2017 and 2018, from 6.9 per cent in 2015.
"Continued implementation of reforms should support the continued rebalancing of domestic demand," the report said on the Chinese economy.
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"In particular, growth in investment and industrial output will moderate, reflecting measures to contain local government debt, reduce excess industrial capacity and reorient fiscal stimulus toward social sectors."
Victoria Kwakwa, incoming World Bank East Asia and Pacific vice president, said in a statement that the region's developing countries accounted for "almost two-fifths of global growth" last year.
The forecasts were made against a backdrop of slowing world growth, weak global trade, low commodity prices and volatile financial markets, with China's economic slowdown a major drag.
Excluding China, regional growth is projected to pick up from 4.7 per cent last year to 4.8 per cent this year and 4.9 per cent in 2017 and 2018, powered by Southeast Asia's robust economies, the bank said.