Three other servicemen were injured in the incident.
The soldier, who has not been named, was involved in a live firing training exercise.
It appears that he was wounded in the incident on Wednesday, but later succumbed to his injuries.
Newly appointed MoD Minister Tobias Ellwood said an investigation is underway.
“It is with deep sadness that I can confirm the death of a soldier from the Royal Tank Regiment who died as a result of injuries sustained in an incident at Castlemartin Ranges,” he said in a statement.
“His next of kin were by his bedside and we will be respecting their privacy before further details are released. Three other soldiers have also been wounded and our thoughts remain with the friends and families of all those involved.
“The safety of our personnel is our absolute priority and a full investigation is underway to understand the details of this tragic incident,” the statement says.
Castlemartin Range Incident – Statement pic.twitter.com/IuKeQeV5MX
— Royal Tank Regiment (@RoyalTankRegt) June 15, 2017
The Royal Tank Regiment (RTR) uses the 63-tonne Challenger 2 battle tank as their main vehicle.
In 2012, a soldier with the Royal Irish Regiment named Michael Maguire was killed during a live firing exercise at the same range. His death was later ruled unlawful by an inquest.