In Japan, the Nikkei 225 dropped 1.35% in early trade as shares of convenience store chain FamilyMart dropped more than 3%. The Topix also declined 1.36%.
Over in South Korea, the Kospi declined 0.74%, with shares of Samsung Electronics falling more than 2%.
The ASX 200 in Australia also shed 0.81% as almost all the sectors traded lower.
Overnight on Wall Street, the Dow had fallen 237.92 points to close at 25,347.77. The S&P 500 also slipped 0.8% to finish its trading day at 2,802.39, while the Nasdaq Composite shed 0.4% to close at 7,607.35.
The yield on the benchmark 10-year Treasury note also dropped to around 2.26%, its lowest level in 19 months. Yields move inversely to prices.
Meanwhile, investors continued watching for developments on the U.S.-China trade front.
U.S. President Donald Trump said Monday the U.S. was “not ready” to strike a deal with China, before adding he expected one in the future. He also said tariffs on Chinese imports could go up “substantially.”
For its part, China appeared to have made a veiled threat concerning rare earth minerals, a crucial component to the U.S. technology industry.
Chinese President Xi Jinping recently visited rare earth mining and processing facilities, adding to speculation that China could make the minerals more expensive or unavailable if the trade war continues to expand.
Shares of Lynas in Australia surged more than 6% in Wednesday morning trade on the back of that development, with the company being one of the few rare earth miners outside of China.
The U.S. dollar index, which tracks the greenback against a basket of its peers, was at 97.912 after bouncing from levels below 97.8 yesterday.
The Japanese yen traded at 109.35 against the dollar after seeing levels above 109.5 in the previous session, while the Australian dollar changed hands at $0.6928 after seeing an earlier low of $0.6917 yesterday.
Oil prices slipped in the morning of Asian trading hours, as the international benchmark Brent crude futures contract slipped 0.21% to $69.96 per barrel. U.S. crude futures also declined 0.56% to $58.81 per barrel.
— CNBC’s Fred Imbert contributed to this report.