Japanese exports rose by just 0.6% in September from a year earlier, much slower than in previous months.
The data is seen as reflecting a slowdown in Japan's top trading partner, China.
However, the Nikkei 225 closed 1.9% higher at 18,554.28 on hopes the weak data would trigger more stimulus efforts from the government.
In China, the mainland's benchmark Shanghai Composite closed down 3.06% at 3,320.68.
Hong Kong's Hang Seng remained closed on Wednesday for a public holiday.
In Australia, the S&P/ASX 200 rose by 0.2%, closing at 5,248.30.
Shares in mining giant BHP Billiton rose 1% after it maintained its full-year production guidance for iron ore.
Slowing growth in China has been weighing on mining stocks in recent weeks as the country is the main importer of Australian commodities.
South Korea's benchmark Kospi index rose marginally by 0.2% to finish at 2,042.98.
Shares of LG Electronics jumped by more than 14%, boosted by a fresh supply agreement with General Motors.
Japanese shares rose on Wednesday, despite news of disappointing export growth last month.