The research firm's purchasing managers' index for the Pan-Asian region fell from 49.3 in June to 48.2 in July.
The index uses 50 as the break-even point between contraction and growth. Higher numbers indicate growth.
"The downturn is being led by falling exports, which deteriorated across Asia at the fastest rate since April 2009," the report said.
Weakened demand from Europe, the United states "and from many Asian markets," slowed exports, the report said.
In July, the PMI "fell further into negative territory in bellwether economies of South Korea and Taiwan, with both seeing the steepest downturns since last December."
In Japan, manufacturing slowed at a faster pace for the second consecutive month. In China, the HSBC index for manufacturing rose from 48.2 in June to 49.3, showing a slowdown for the second consecutive month, despite the improvement.
The PMI index remained positive -- that is, above 50 -- in India, but fell from 55 to 52.9.
In Indonesia, the PMI rose from nearly break-even, 50.2, to 51.4.
In South Korea, the PMI dropped from 49.4 to 47.2. In Japan it dropped from 49.9 to 47.9.
In Vietnam, the PMI fell from 46.6 to 43.6.