The Shanghai composite fell 3.72 percent to close at around 2,716.51 — which marked its largest decline since June 19, according to Chinese financial services firm Wind Information. The Shenzhen composite dropped by 3.834 percent to end at about 1,386.28 on the first trading day since the Golden Week holidays ended. As of 3:21 p.m. HK/SIN, Hong Kong's Hang Seng index traded lower by 1.2 percent.
The People's Bank of China announced on Sunday it was cutting the reserve requirement ratio (RRR) — or the amount of cash that banks have to hold as reserves — by 100 basis points effective Oct. 15. The RRR is currently 15.5 percent for large commercial banks and 13.5 percent for smaller lenders.
The move by China's central bank, its fourth in 2018, came amid concerns about the economic impact of Beijing's ongoing trade war with Washington.
All the major Chinese banks saw sharp declines on Monday. Industrial and Commercial Bank of China fell by 3.64 percent, China Construction Bank tumbled by 4.28 percent while Agricultural Bank of China lost 2.57 percent.
Australia's markets also ended the day lower with the ASX 200 shedding 1.38 percent at 6,100.3, with major sectors lower.
The heavily-weighted financial sector closed lower by 1.33 percent, with shares of Australia and New Zealand Banking Group (ANZ) falling by 2.63 percent and Commonwealth Bank of Australia lower by 0.93 percent. The movement in ANZ's stock came after it announced that its full year 2018 cash profit would be "impacted by additional charges for customer compensation, accelerated amortisation of software and other notable items."
Other Asian markets were also in negative territory. South Korea's Kospi slipped by 0.6 percent to close at 2,253.83, while shares of industry heavyweight Samsung Electronics held on to gains of 0.56 percent.
Stocks of companies under the Lotte Group also rose following its Chairman Shin Dong-bin's release from prison last Friday after a court suspended his jail sentence for a crime linked to former South Korean President Park Geun-hye. Lotte Confectionery saw gains of 2.68 percent, while Lotte Himart advanced by 1.08 percent and Lotte Chemical jumped by 3.05 percent.
Japan's markets are closed for a public holiday.
Currencies and oil
Last Friday, yields on the U.S. 10-year Treasury note also hit a new 7-year high before settling at around 3.233 percent on the back of unemployment stateside falling to its lowest levels since 1969.
The Japanese yen saw a recovery to trade largely flat at 113.76 against the dollar, while the Australian dollar continued to trade stronger at $0.7059, as of 3:16 p.m. HK/SIN.
In the oil markets, prices remained lower. As of 3:17 p.m. HK/SIN, the global benchmark Brent crude futures contract slid by around 1 percent to $83.33 per barrel, while the U.S. crude futures contract was still lower by 0.78 percent at $73.76 per barrel. The moves came after a U.S. government official said on Friday that the Trump administration is considering waivers on the country's impending sanctions on Iran in November.
— CNBC's Fred Imbert and Reuters contributed to this report.
Correction: This article has been updated to reflect that the Shanghai composite on Monday marked its largest decline since June 19, according to Chinese financial services firm Wind Information.