The cargo will be sent to the Tokyo Electric Power Company, the same firm which took receipt of the project's first LNG cargo in May 2014.
ExxonMobil PNG managing director Andrew Barry said the shipment reinforced the reliability of Papua New Guinea's gas production.
"Since export operations began, an LNG carrier has been loaded on average every three to four days with continuous operational excellence," he said.
"This achievement is the result of an excellent performance delivery by world-class facilities and an exceptional workforce."
More than 7 million tonnes of LNG has been exported since production started in April 2014, with the PNG LNG project expected to produce upwards of 9 trillion cubic feet of gas over 30 years.