The genus Eohyrax was first described in 1901 by Florentino Ameghino, based on fossils found in Late Eocene terrains of Argentina.

Ameghino thought the fossils dated from the Late Cretaceous, and this assumption was only corrected much later.

Similarly, Ameghino thought that some of the South American mammals he described were the ancestors of the fauna of other continents, and therefore considered Eohyrax as a relative of hyraxes, hence its name, Eohyrax, meaning "Hyrax of the dawn".

The real affinities of Eohyrax within Notoungulata were only recognized later, as it was reclassified as a member of the subgroup of rodent-like notoungulates Typotheria.

Eohyrax was approached of the genus Archaeohyrax within Archaeohyracidae a family thought to be ancestral to Hegetotheriidae ; however, further researches tend to indicate that Archaeohyracidae are a paraphyletic group, and that Eohyrax itself would be a basal member of a clade including Mesotheriidae and Hegetotheriidae.