The shooting happened at RAF Tain near Inverness, which is used for training exercises.
The soldier, who has not been named, was taking part in an exercise involving about 20 military personnel after sunset on Tuesday at RAF Tain, a large bomb, strafing and live fire training range 30 miles north of Inverness.
Another person is thought to have been injured in the drill and officers remain on the scene. But, there was no threat to the public.
Sky News Scotland bureau chief James Matthews said both were Army soldiers.
Police Scotland said one person had died but there were "no other casualties as a result of the incident".
The Ministry of Defence confirmed his identity this morning, saying he was a member of 3rd Battalion The Rifles who are based at Dreghorn Barracks in Edinburgh and recruit largely in Yorkshire and the north-east of England.
BBC Scotland's Craig Anderson says: "Sometimes this place has a very uneasy relationship with the local community, who obviously have some concerns about low flying. It would be inappropriate for us to comment further at this point".
However, the range is mostly used by Typhoons and Tornados from RAF Lossiemouth.
Just five days ago local MP Dr Paul Monaghan expressed concern that the RAF were being allowed to used the bombing range at Tain and that now the USA airforce was being allowed to do the same.
Mr Rhind said the Tain range has a "very good safety record" and he could not recall any similar incidents.
The range has 18 separate targets suitable for a variety of weapons and delivery methods and it is maintained by the Defence Infrastructure Organisation. Tain is also responsible for Cape Wrath range near the village of Durness.
The death comes just over two months after a soldier was shot dead during a live-firing exercise at Otterburn Training Area in Northumberland.
Earlier this year Cpl Joshua Hoole, 26, of Ecclefechan, near Lockerbie died during training in Brecon, Wales.
"Police Scotland are leading the investigation to establish the full set of circumstances of this incident and we are working closely with the Crown Office and Procurator Fiscal Service, the Health and Safety Executive, and the Armed Forces".