The official purchasing managers' index (PMI) on Sunday showed that factory activity unexpectedly shrank in October to 49.8, below the 50-point mark, which suggests contraction.
It is also marks the third consecutive month of contraction in manufacturing.
The Shanghai Composite closed down 1.7% to 3,325.08, while Hong Kong's Hang Seng closed down 1.2% at 22,370.04.
A private survey, which focuses on smaller to mid-size firms, also showed on Monday that factory activity fell for the eighth month in a row in October, but it was an improvement from the previous month.
The Caixin/Markit manufacturing PMI was up to 48.3, from 47.2 in September.
Angus Nicholson, market analyst at trading firm IG, said manufacturing activity in China should pick up in the last few months of the year.
"The key takeaway from the manufacturing PMIs is that activity in China has stabilised in the wake of significant monetary easing and fiscal spending," he said in a note.
Japan's benchmark Nikkei 225 index ended down 2.1% to 18,683.24 - leading the losses in the region.
Investors will be watching shares of Nissan after it posted a rise of 37.4% in net income for the six months ending in September.
The focus will also be on US data, with key employment figures due on Friday, which could influence the timing of the Federal Reserve's highly anticipated decision to raise interest rates.
In Australia, the benchmark S&P/ASX 200 closed down 1.4% to 5,165.80 ahead of the central bank's decision on interest rates on Tuesday.
The Reserve Bank of Australia (RBA) is expected to keep interest rates at a record low of 2%.
Westpac shares were down 2.5% after it wrapped up Australia's bank reporting season, seeing a 3% rise in its annual cash profit.
The country's four major banks are preparing for their slowest earnings growth since the global financial crisis, due to low interest rates and a cooling economy.
Bucking the trend, South Korea's Kospi index finished up 0.3% to 2,035.24 points.

Launching its general election manifesto, party leader Leanne Wood said she wanted an "end to austerity".
Ms Wood said the four Westminster leaders offered "nothing more than further swingeing cuts" to voters.
Plaid says it will negotiate jointly with the SNP and the Greens if there is a hung parliament.
Plaid Cymru wants the devolved Welsh government funded to the same level per head of population as the Scottish government - which it says amounts to £1.2bn extra a year.
At the party's launch event in Bangor, Ms Leanne Wood accused the UK parties of giving "no commitment to securing an economic recovery for all".
Plaid wants to restore the 50p income tax rate for earnings above £150,000, increase National Insurance contributions for higher earners and put a tax on sugary drinks.
Ms Wood also pledged to create up to 50,000 jobs by awarding more public contracts to Welsh firms.
Main pledges
Plaid's manifesto contains plenty of familiar territory but there's no mention of the £1.2bn which is repeatedly referred to by Leanne Wood as the extra funding Wales needs to achieve parity with Scotland.
It talks about the creation of an independent commission to resolve funding issues in future.
Elsewhere, there are plans to reintroduce the 50p top rate of income tax.
Independence is not mentioned until page 36 out of a 64 page document, and then only briefly.
Asian markets started the week with losses as investor confidence was dented by China's manufacturing data.
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Plaid Cymru has promised more cash for Welsh public services, an extra 1,000 medical jobs and to scrap taxes for 70,000 small businesses.