Last week, the US dollar fell to a 15-month low against the yen and the Nikkei index lost more than 11%.
On Monday, however, the dollar rose to 113.95 yen from 113.25 yen on Friday in New York.
The bounce for the Tokyo market came despite official figures showing Japan's economy had contracted by 0.4% in the three months to December.
The worse than expected quarter-on-quarter figures did not stop the Nikkei 225 closing 7.2% higher at 16,022.5 points - its biggest daily percentage gain since late 2008.
Last week, Japan's markets traded sharply lower as a stronger yen against the dollar hurt the country's big exporters.
On Friday the Nikkei index closed down 4.8% to 14,952.6 points - below the 15,000 points level and its lowest close since October 2014.
But a retreat of the yen on Monday sent shares in the country's big exporters sharply higher.
Toyota finished the trading day in Tokyo up more than 9.5%, Honda gained 8% and Nissan rose 6.7%. Sharp and Sony gained just over 7% and 8% respectively.
Analysts said the yen could continue to weaken this year, which would be good for exporters.
"We retain our view that the yen will weaken towards 130 against the dollar by year-end, from 113 today," said Marcel Thieliant from Capital Economics.
The yuan was on track for its biggest daily gain in about 10 years on Monday, analysts said
Elsewhere, markets in China were divided despite worse-than-expected trade numbers.
On the mainland, where markets were open after a week off for Lunar New Year celebrations, the Shanghai Composite closed down 0.6% at 2,746.2.
In Hong Kong, however, the Hang Seng jumped 3% to 18,874.5 points after finishing lower on Thursday and Friday.
Trade numbers released on Monday showed China's exports in yuan terms fell 6.6% in January from a year earlier, while imports dropped 14.4%.
In US dollar terms, exports fell 11.2% from a year earlier and imports fell 18.8%, marking the seventh and 15th month of straight declines respectively.
The numbers mean the country was left with a record trade surplus of $63.3bn for the month, compared to $60.9bn in December.
Analysts said the January trade data was a reflection of slower external demand - particularly from trading partners like South Korea.
In Australia, the benchmark S&P/ASX 200 finished up 1.6% to 4,843.5 points, while South Korea's benchmark Kospi index closed up 1.5% to 1,862.2 points.
BBC News