The preliminary Caixin manufacturing purchasing managers' index (PMI) fell to 47 in September, below forecasts of 47.5 and down from 47.3 in August.
A reading below 50 indicates contraction in the sector, while one above shows expansion.
The Shanghai Composite dropped 2.2% to 3,115.89 on the disappointing data.
The private survey also marked the seventh consecutive month of contraction in the sector.
In Hong Kong, the Hang Seng index closed down 2.3% at 21,302.91.
Japanese markets are closed for a three-day public holiday and will reopen on Thursday.
In Australia, shares in mining companies were hit by falling commodity prices.
Oil prices continued to decline after US crude fell 2% overnight on global growth concerns, while copper prices slipped further on slowing Chinese demand.
Sydney's S&P/ASX 200 index closed down 2.1% at 4,998.10.
In South Korea, the Kospi index ended 1.9% lower at 1,944.64 following the release of the data from China.
Asian markets headed lower after a survey of China's manufacturing sector indicated it is shrinking at the fastest pace for six-and-a-half years.