The Nikkei 225 index was down 3.0 percent shortly after opening. In the afternoon, after the Trump tariffs came into effect, it was at minus 4.9 percent. Taiwan's Taiex index had then fallen to minus 5.8 percent.
The broader Topix index initially indicated a minus 2.1 percent.
A more significant decline is seen particularly among Japanese exporters, since the Japanese yen strengthened more than 1 percent against the dollar overnight to Wednesday local time.
In Hong Kong, the Hang Seng index was also sharply down, 4.1 percent in the initial trading – but there was a partial recovery to 1.6 percent by lunchtime.
The Shanghai and Shenzhen composite indices had retreated 0.4 and 0.3 percent, respectively.
The Asian stock market follows Tuesday's volatile trading on Wall Street, where the leading indices fell significantly after the White House announced that Donald Trump's threat of import tariffs of 104 percent on goods from China would become a reality from midnight local time.
This despite China saying on Tuesday that the country is ready to "fight to the end" if Trump makes good on his threats.
The broad S&P 500 index closed at minus 1.6 percent, the Nasdaq composite index 2.2 percent, and the Dow Jones industrial index 0.8 percent.
