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.

The Eastern Europeans are a coming force in rugby union and have aspirations of playing in the Six Nations.
They are 12th in the world rankings - two places above Italy - but have played top-tier nations only four times outside of World Cups.
Wales will also face New Zealand, Australia and South Africa in November.
Wales won three of their four autumn fixtures in 2016, beating South Africa, Japan and Argentina after losing to Australia.
Georgia have won the Rugby Europe Championship - Europe's second-tier competition below the Six Nations - for the last six seasons in succession.
They have already qualified for the 2019 World Cup in Japan having finished third in their group in the last tournament in England.
That campaign included a win over Tonga, while Georgia have also beaten Fiji and drawn with Samoa during the last year.

Liberal Democrat leader Tim Farron called Labour "careless" for spending European Union (EU) money on ineligible projects and the Conservatives "mean-spirited" to use flood relief money to repay the wrongly used funds.
The government blamed Labour's "mismanagement" of the money.
Labour has been approached for comment.
Local government minister Andrew Percy, revealed in a written statement that £15m EU Solidarity Funding received in respect of the winter 2015-16 floods would be "offset" by the £14.5m repayment.
The UK was "legally obliged" to make the repayment because there had been "ineligible spending under the Labour administration" of 2007 funding.
The remaining £500,000 was "only eligible to reimburse" the government for financial support given to affected areas, he said.
Westmorland and Lonsdale MP Mr Farron said the two parties had "combined to deprive flood-hit areas of much needed funds".
"Labour's overspending has hurt the North and all those affected by last year's floods," he said.
"But it is the Conservative's mean-spiritedness which means they have chosen to use this money to pay the fine, instead of passing this money on to flood-affected areas and paying the fine from Treasury coffers."
In response, Mr Percy said the government had delivered £300m to help flood-hit communities.
"Liberal Democrats are misleading the public by suggesting there's some EU magic money tree," he said.
Japanese shares rose on Wednesday, despite news of disappointing export growth last month.
[NEXT_CONCEPT]
Wales will play Georgia for the first time at the Principality Stadium in the 2017 autumn series.
[NEXT_CONCEPT]
About £15m of funding intended for UK communities hit by floods last winter will instead be used to cover a "fine" for misspending a previous grant.