The region is now expected to grow by 5.8% this year and 6% in 2016, revised down from March's forecast of 6.3% for both years.
The bank said China's slowing growth would affect demand in Asian economies.
It expects the world's second largest economy to grow by 6.8% this year, below the government's forecast of 7%.
China's economy grew by 7.3% last year and the ADB expects its growth to slow even more next year to 6.7%.
Earlier this month, the International Monetary Fund flagged that slower Chinese growth posed a threat to the global economy, as it would reduce demand for commodities from other economies.
The US Federal Reserve held off raising interest rates for the first time in nearly a decade last week, in part due to concerns over the impact of the slowdown in China.
The Philippines-based ADB also highlighted that slowing growth in the another Asian powerhouse - India - would weigh heavily on the region.
It expects growth in India to slip to 7.4% this year from an earlier forecast of 7.8%, due to weaker external demand and slower reforms "holding back" India's economy.
"To counter the impacts of a US rate rise, monetary policy authorities in developing Asia will need to find a balance between stabilising the financial sector and stimulating domestic demand," the report said.
Policymakers in both China and India have cut interest rates several times this year, among other measures, in an attempt to boost lending and lift consumer demand.
The Asian Development Bank has lowered its growth forecasts for Asia's developing economies on the back of slowing growth in both China and India.