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.
Asian markets started the week with losses as investor confidence was dented by China's manufacturing data.