The soldier, a woman in her 40s from the Jämtland region, died in an accident involving a combat vehicle of the CV90 model near Överkalix just before 1am on Monday, said the Swedish Armed Forces.
Emergency services were called to the scene, but her life could not be saved.
Nobody else was injured in the incident.
Around 10,000 people, including 3,000 Swedes, are taking part in Northern Wind. The exercise is scheduled for March 18th-27th and also involves soldiers from Finland, Norway, the UK and USA.