Greek a- a- entry 2 + xénos "foreigner, guest" + -ic entry 1 — more at xeno-
Note: The term was introduced by the American biologist James A. Baker (1910-75) and his Rockefeller Institute co-worker M.S. Ferguson in the article "Growth of Platyfish (Platypoecilus maculatus) Free from Bacteria and Other Microörganisms," Proceedings of the Society for Experimental Biology and Medicine, vol. 51 (October, 1942), pp. 116-19. The authors thus etymologize the word in a footnote: "Axenic is derived from two Greek words: A—meaning without or free from, and Xenos—denoting a stranger or foreign life. An axenic organism, as here defined, is a species free from any life apart from that produced by its own protoplasm …The writers are greatly indebted to Professor A.C. Johnson, Department of Classics, Princeton University, for suggesting and defining the term axenic."