[2] Fossils of the species were found in 2002 and 2005 at a site 1.5 kilometres northeast of Faxinal do Soturno, Rio Grande do Sul, from the Caturrita Formation dating from the Carnian-Norian, 220–215 million years old.

The holotype, UFRGS PV0927T, is part of the collection of the Universidade Federal do Rio Grande do Sul and consists of several, partially fragmentary, limb elements, perhaps of a single individual.

The describers assigned Faxinalipterus to the Pterosauria, based on its long hollow limbs and saddle-shaped upper joint of the relatively short and robust humerus, suitable to perform a wing stroke.

However, Alexander Kellner has suggested Faxinalipterus might be not be a pterosaur but a basal member of the Pterosauromorpha instead or, if the lack of fusion between tibia and fibula is plesiomorphic, even a sister taxon of the Ornithodira.

[3] Faxinalipterus was reinterpreted as an early member of Lagerpetidae by Kellner and colleagues in 2022, who also removed the maxilla from the referred specimens and assigned it to the newly named basal pterosauromorph Maehary.