It follows big falls in US and European markets on Thursday, with the Dow Jones dropping more than 2%.
China's Shanghai Composite index closed down 4.27% at 3,507.74 points.
Data released on Friday morning showed Chinese factory activity falling to its lowest level in more than six years.
The private Caixin/Markit manufacturing purchasing managers' index (PMI) dropped to 47.1 from 47.8 in July. A figure below 50 shows contraction in the sector and one above means growth.
As domestic and export demand dwindle, Friday's data is likely to add to global worries that the Chinese economy is set for a continued slowdown.
In Hong Kong, the Hang Seng index followed the mainland's trend and was 1.53% lower at 22,409.62 points.
Asia's largest stock market, Japan's Nikkei 225 index, dropped sharply, finishing 2.98% down at 19,435.83 points.
The sell-off in Japan stretched across most blue chip stocks, with carmakers Toyota, Nissan, Honda and Mazda all shedding as much as 3% in early trading.
Among the country's technology giants, Sony saw the sharpest drop with shares down by more than 4%.
Markets worldwide have become increasingly nervous over prospects for the global economy, especially with signs that the Chinese economy is slowing.
The devaluation of China's currency, the yuan, last week took many by surprise, and the Chinese stock market has continued to see big fluctuations despite efforts by Beijing to calm markets.
In South Korea, the Kospi index followed Tokyo's lead, finishing 2.01% down at 1,876.07, with most of the country's main stocks being pulled lower.
Australia's S&P/ASX 200 also closed in negative territory, falling 1.4% to 5,214.60.
Shares in oil and gas company Santos started to climb back up after reaching a 12 year low in early trading, but closed down 0.2%.  Its half year profits came in well below forecasts.
It has appointed a new executive chairman to try and turn around its fortunes.
Asian stocks saw sharp falls on Friday as mounting concerns over China's slowing economy continued to affect global markets.