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.

The 22-year-old has not appeared for Shrewsbury this season, but has played once for Mansfield Town and four times for Wrexham while on loan.
Bolton youth product Caton has also played for Blackpool and has loan spells with Accrington and Chester before joining Shrewsbury in 2014.
Caton follows Jamie McCombe, 33, in signing for the National League side.
The centre-back, who played 101 games for the club during his first spell, has left Stevenage and signed a contract until the end of the 2016-17 season.

Mr Blunkett said using the same funding formula applied to Wales - which has a devolved budget - Yorkshire would be entitled to a Â£24bn budget.
"You put great store by devolving decision-making to ordinary people," he told Prime Minister David Cameron.
Mr Cameron said the government had already got rid of a "centralised" approach that Mr Blunkett was part of.
Mr Blunkett, a Labour former Cabinet minister and the MP for Sheffield Brightside and Hillsborough, made the suggestion during prime minister's questions in the House of Commons.
He said: "Can you think of one single reason why the people of Yorkshire shouldn't determine their own priorities?
"And, mischievously, one reason why the people of Yorkshire shouldn't have their own White Rose Parliament?"
Mr Cameron said: "What we are doing is we are saying to councils in Yorkshire, as up and down the country, 'We are getting rid of the ring fences, we are giving you the power to spend your money in the way that you choose'."
He added: "We have got rid of the bossy, centralised interfering approach that I'm afraid you were rather part of."
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.
[NEXT_CONCEPT]
Lincoln City have signed Shrewsbury winger James Caton on loan until the end of the season.
[NEXT_CONCEPT]
Yorkshire should be given its own "White Rose Parliament" with its own budget, MP David Blunkett has said.