Corporal Brendan Hannam was killed during an exercise at the Mount Bundey training area in the Northern Territory on Monday evening.
The 28-year-old father of two was a passenger in a Supacat troop-carrying vehicle at the time of the incident.
Five other army personnel were injured.
Defence Minister Richard Marles said operational use of the vehicle had been put on hold while an investigation into the death was carried out.
"We need to be making sure that every lesson that can be learned from this incident is learned," he told reporters in Perth on Wednesday.
"We've paused operational use of that vehicle until the investigation has commenced to understand what, if anything, may be impacted."
The Supacat is an all-terrain vehicle used by special forces units and the army's first brigade.
Chief of Army Susan Coyle said suspension of the vehicle's use during the investigation was standard practice following a training incident.
She confirmed the five other army members who were injured in the incident remained in hospital.
Two of them are in Royal Darwin Hospital and three are in the Robertson Barracks medical centre.
The Mount Bundey area, about 120km south of Darwin, is used for Australian and US forces training, including live-fire exercises.
Mr Marles said he had spoken with defence force head Mark Hammond about what could be done to improve safety during training exercises.
Aspects such as risk settings and fatigue management would be the focus of the review.
"The training is dangerous work, it does carry risk," the defence minister said.
"Monday was very much a reminder of that."
The death comes months after a defence force member was killed in a training exercise in Jervis Bay.
Warrant Officer Class Two Lachlan Muddle, a Special Air Service Regiment operator, died after colliding with a fellow soldier during a parachuting exercise.
In October 2025, a soldier died and two others were hospitalised after a truck rolled over during an army training course.
Jack Fitzgibbon, the son of former defence minister Joel Fitzgibbon, died in March 2024 after a parachuting incident at the Richmond RAAF base outside of Sydney.
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