The forecast announced by the Manila-based bank in its Outlook 2102 was revised down from its earlier one in which it called for 6.9 percent in 2012 and 7.3 percent in 2013.
The region registered growth of 7.2 percent in 2011.
The bank said after years of rapid growth, "the region must brace for a prolonged period of moderate expansion amidst an ongoing slump in global demand."
ADB's chief economist, Changyong Rhee, said countries in developing Asia also will need to do more to reduce reliance on exports, rebalance their sources of growth, and increase their productivity and efficiency.
"These measures are critical if the region is to continue lifting its people out of poverty," he said.
The report said the deceleration of the region's two giants, China and India, has come about in tandem with the global slowdown for any early optimism.
It warned the sovereign debt crisis in the eurozone and the looming fiscal cliff in the United States could have "disastrous spillovers" in the rest of the world, especially developing Asia.
On the plus side, the report said the Asian slowdown is likely to ease price pressures, with inflation falling from 5.9 percent in 2011 to 4.2 percent in both 2012 and 2013, provided there are no spikes in international food and fuel prices.
The ADB said China's GDP is forecast to grow 7.7 percent this year and 8.1 percent in 2013, down from 9.3 percent in 2011.
India's GDP was forecast to slow to 5.6 percent this year from 6.5 percent in 2011.