The woman and her companion – a 53-year-old man who was unharmed – were descending in the area of the Gran Diagonal, Spanish news outlet El País reported.
Members of the Mountain Rescue and Intervention Group (GREIM) attended the scene, as well as the Huesca Air Unit.
The woman, a British national who lived in Finland, was pronounced dead and her body was taken to Zaragoza’s Forensic Medicine Institute for a post-mortem.
A Foreign Office spokesperson said: “We are aware of a British woman who has died in Spain and are in contact with the local authorities”.
An investigation is ongoing, a spokesperson for the Civil Guard told The Sun.
They said a report would be sent to a “local investigating court along with the post-mortem results”.
The woman’s death is being treated by the force as a “tragic accident resulting from a fall”, they said.
The incident follows several other interventions by the Civil Guard’s mountain team in the Pyrenees in the past week.
Between 26 May and 30 May, the GREIM carried out nine mountain rescues.
On Monday, the Civil Guard called for hikers to take safety precautions before heading out into the mountains.
It encouraged them to bring enough water, take charged electronics with location settings enabled, wear sun protection, and to check the route and weather before setting off.