1886, "a devotee of the teachings of German political theorist Karl Marx" (1818-1883), from French marxiste. The adjective, "of or pertaining to the socialist doctrines and theories of Karl Marx," is attested from 1884. The alternative adjectival form Marxian (1887 in reference to Karl Marx) sometimes is used (1940, by Groucho, among others) to distinguish the U.S. vaudeville family from the German political theorist.
word-forming element making nouns implying a practice, system, doctrine, etc., from French -isme or directly from Latin -isma, -ismus (source also of Italian, Spanish -ismo, Dutch, German -ismus), from Greek -ismos, noun ending signifying the practice or teaching of a thing, from the stem of verbs in -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached. For distinction of use, see -ity. The related Greek suffix -isma(t)- affects some forms.
<a href="https://www.etymonline.com/word/Marxism">Etymology of Marxism by etymonline</a>
Harper, D. (n.d.). Etymology of Marxism. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/Marxism