The incident occurred yesterday morning in Bahir Dar, a leading tourist destination about 500 kilometres (300 miles) from the capital Addis Ababa and famed for the nearby Lake Tana, the source of the Blue Nile.
"It appears that a resident of Bahir Dar, who was licensed to carry a gun, accidentally discharged his gun while changing the gun position from one shoulder to the other," government spokesman Shimeles Kema said.
"The gun is an old rifle," he said, adding that the man did not know it was loaded.
The British embassy confirmed that a national had died but gave no details.