Shipments shot up 10.1% from the previous year, data showed, to earn 5.8tn yen ($60.5bn; £39bn).
The yen has weakened significantly since last year, despite recent gains, helping exporters.
A strong yen makes their goods expensive overseas and cuts profits.
“This (export data) shows Japanese companies are increasingly in better shape,” said Junko Nishioka, chief economist at RBS Securities Japan. “Their profitability is also rising these days, meaning they are becoming more resilient to potential external shocks.”
Shipments picked up in key markets, with exports to the US rising 16.3% from a year earlier. Shipments to China increased by 8.3%.
The yen has lost more than a fifth of its value against the US dollar in the 12 months to May. Even though it has gained some strength in recent days, it is still 17% below where it was a year ago and currently trades at about 95 yen to the dollar.
Many Japanese firms have said this is the right level for their exports to recover.