By Agence France-Presse
The Nikkei 225 index fell 1.77 percent or 401.85 points to close at 22,278.48 while the broader Topix index was down 1.55 percent or 27.51 points at 1,743.92.
The market was under pressure after Trump unveiled plans to impose 10 percent tariffs on $200 billion worth of Chinese goods over Beijing's "unacceptable" move to raise its own tariffs.
The US leader warned that after the new measures are in place -- on top of existing 25 percent tariffs on $50 billion in Chinese imports -- tariffs on another $200 billion would go forward "if China increases its tariffs yet again."
SBI Securities said the growing trade war had driven investors to the sidelines "as it is hard to tell how the escalating trade frictions between the United States and China will affect Japan."
The Japanese currency rose on safe-haven buying, with the dollar buying 109.61 yen against 110.56 yen in New York on Monday afternoon.
"As the dollar fell below 110 yen, market sentiment deteriorated," Shinichi Yamamoto, broker at Okasan Securities in Tokyo, told AFP.
In Tokyo trading, Japanese flea market app Mercari soared 76.7 percent from its IPO price to close at 5,300 yen as it debuted on the Tokyo Stock Exchange.
"Mercari got off to a flying start" with investors impressed by its successful business model, Yamamoto said.
Companies with strong business ties with China fell. Komatsu dropped 2.48 percent to 3,180 yen and Hitachi Construction Machinery slipped 1.52 percent to 3,560 yen.
Fujifilm lost 1.56 percent to 4,215 yen after it filed a lawsuit against Xerox in New York, seeking $1 billion in damages after the US giant scrapped a merger with it.