Arcticodactylus is known from a single partial specimen from the Late Triassic Fleming Fjord Formation of eastern Greenland. The specimen is disarticulated and made up of portions of the skull, vertebrae, and ribs, part of the right shoulder and wing, and portions of both legs. Arcticodactylus was named in 2001 by Farish Jenkins and colleagues as a new species of Eudimorphodon, E. cromptonellus. In 2015, the species was reanalyzed by Alexander Kellner and given its own genus, Arcticodactylus.
The skull is known from several disarticulated bones including the tooth-bearing bones of the upper jaw. The teeth are unusual, and bear multiple cusps. Those teeth near the tips of the jaws are simplest, with one of two cusps, but those in the middle portion of the tooth row have as any as five cusps. Additionally, there appears to be a wide gap, known as a diastema, between the third and fourth teeth.
The proportions of the limb bones are unique, with humerus, ulna, femur, and tibia being roughly the same length. Like all Triassic pterosaurs, Arcticodactylus had a long tail. The specimen is of a very small individual, with a wingspan of only about 24 cm (9.5 inches), similar to an American robin. Detailed examination of the bones suggest that it was partially grown, and would have likely been larger as an adult.
Arcticodactylus is a eudimorphodontid, from a family of small Triassic pterosaurs known largely from Europe. They are characterized by their multi-cusped teeth, although unlike Arcticodactylus, many species have fang-like teeth throughout the tooth-row. They may have taken a large variety of food items, from fish to insects to plants, and used their teeth to chew. Arcticodactylus may have had a unique and unusual diet, due to the diastema and tooth-row without fangs.