At the time of the conquest, the village belonged to Mencey (King) Acaymo of Güimar, bordering on the extensive district of Abona or Chasna.
Several writers mention Fasnia in the 16th century, pointing out that it was inhabited by real Guanches and that the conquistadors had not ventured beyond Güimar. A traveller of the time reported caves that acted as dwellings.
There are several versions of the appearance of the Patron Saint of the parish, San Joaquín; but, in general, it was exchanged for an animal, probably a kid. The figure was placed in a cave and later transferred to the old church.
The church of San Joaquín belonged to the parish of San Pedro Apóstol, in Vilaflor, and then to the parish of Lomo de Arico, until it was granted the status of parish church in 1796. The local population then decided to build a new church on the present site. This was burned down in 1918 and rebuilt.
Fasnia already had a district Mayor when the church was made a parish church and, in 1814, it separated from Arico. There is a document dated 1923 that mentions the dissolution of the existing Council and the creation of a new one, that initially had to meet in private houses as there was no Town Hall.