The Nikkei 225 index ended 3.1% lower at 16,174 – higher than its low point for the trading session, but still the lowest close since April 12.
Toyota shares closed down 3.8%, Nissan Motor dropped 5% and Honda Motor shed 4%.
The yen shot up after the Bank of Japan (BOJ) decided not to launch fresh economic stimulus last week.
On April 29, the yen was at about 108 yen against the dollar. It strengthened a little on May 2 to around 106.31 yen.
In South Korea the Kospi ended May 2 session lower, by 0.8% at 1,978.15 points. And that is also a three-week low.
Markets in China and Hong Kong are shut on May 2 for the Labor Day holiday.
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