The type species, Moschowhaitsia vjuschkovi, was discovered in the Changxingian-aged Archosaurus Assemblage Zone of Russia and named in 1963 by Russian palaeontologist Leonid Petrovich Tatarinov.

[1][2] The genus name Moschowhaitsia alludes to two other therocephalians, Moschorhinus and Whaitsia (a junior synonym of Theriognathus), due to the structure of its palate combining physical features of both these genera.

[3] Some later researchers, including Tatarinov himself, would later elevate Moschowhaitsia to family level distinction (Moschowhaitsiidae), along with other subtaxa of whaitsiids, although nonetheless retaining the existing close taxonomic relationships under the superfamily Whaitsioidea.

[4][5] However, later research of therocephalian evolution using cladistics regardless of taxonomic ranking have found that many of the various whaitsiids/whaitsioids are in fact only distantly related to each other, with many belonging to the earlier-diverging clade Akidnognathidae instead (including members of Moschorhininae).

[6] A cladogram depicting the relationships of both M. vjuschkovi and M. lidaqingi is shown below, reproduced from Liu & Abdala (2023) and simplified to show the relationships of whaitsioid therocephalians:[2] Scylacosuchus Akidnognathidae Nanictidops Perplexisaurus Purlovia Caodeyao Ophidostoma Hofmeyria Mirotenthes Ictidostoma Ictidochampsa Microwhaitsia Viatkosuchus Theriognathus Moschowhaitsia vjuschkovi Moschowhaitsia lidaqingi Ichibengops Chthonosaurus Baurioidea The strict-consensus tree shown above did not recover M. vjuschkovi and M. lidaqingi as each other's sister taxa (found as such in only six of the 30 most parsimonious (i.e. shortest) trees).