1928, in reference to galaxies as presently understood, from inter- + galactic. The word itself was in use by 1901, when galaxies were thought to be a sort of nebulae.
Entries linking to intergalactic
inter-
word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."
A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
galactic adj.
1839, "of the Milky Way, of the bright band of stars around the night sky," from Late Latin galacticus, from galaxias (see galaxy). In modern scientific sense "pertaining to (our) galaxy," from 1849. From 1844 as "of or pertaining to milk."