Police said the 42-year-old man, who has not been named, was hiking with a companion in the Tyrol region in western Austria on Friday.
Neither was an experienced climber, according to police.
The Foreign Office confirmed it was communicating with the Austrian authorities.
A spokeswoman said: "We can confirm the death of a British national in Austria. We are providing consular assistance to the family."
The official tourism website for the area said it is popular with novice hikers and seasoned climbers, with a rating system that includes "easy" hiking trails, moderate mountain footpaths and "extreme" Alpine routes.