Both Hong Kong’s Hang Seng index and the Shanghai Composite fell by more than 1.6%, and the benchmark Nikkei 225 closed down 1% as well.
On Monday, Japan revised down its 2013 growth estimates and reported a record deficit.
Over the weekend, China said exports plunged 18.1%, surprising analysts.
The country also reported a rare $22.98bn trade deficit in February, compared to a surplus during the same period last year.
Some analysts speculated that the figures could be distorted due to the impact of the Chinese Lunar New Year holiday.
China also reported a slowdown in inflation, to 2% in February from 2.5% in January – the slowest rate in 13 months.
The sluggish economic data come as the Chinese government said during its annual meeting that it was targeting a growth rate of 7.5% in 2014.
However, China’s finance minister Lou Jiwei later said that it would be acceptable if the government slightly missed this target.
“Whether GDP [gross domestic product] growth is to the left or to the right of 7.5%, that is not very important,” said Mr Lou, according to Reuters.
He added that what was most important was job creation.
Separately, Japan revised its 2013 economic growth from 1% to 0.7%, and also reported its largest deficit since 1985.