The island cowfish was first formally described in 1863 as Ostracion notacanthus by the Dutch physician, herpetologist and ichthyologist Pieter Bleeker, with its type locality given as Saint Helena.

[3] The 5th edition of Fishes of the World classifies the genus Acanthostracion in the within the family Ostraciidae in the suborder Ostracioidea within the order Tetraodontiformes.

Bleeker originally proposed this taxon as a subgenus of the genus Ostracion The Specific name, nothacanthus, combines notos, which means "back" with acanthos, meaning "spine" or "thorn", a reference to the spine-like projection on the third plate-like scale of the carapce from the origin of the dorsal fin.

The overall colour is yellowish with each plate-like scale of the carapace, which covers most of the body, having an frequently incomplete dark margin which may be rounded or polygonal.

It is found at depths between 3 and 25 m (9.8 and 82.0 ft) over rocks, rubble and sand, and has been recorded on shallow reefs.