early 15c., "public disgrace, dishonor, evil fame," from Old French infamie "dishonor, infamous person" (14c.) and directly from Latin infamia "ill fame, bad repute, dishonor," from infamis "disreputable, notorious, of ill fame," from in- "not, without" (see in- (1)) + fama "reputation" (from PIE root *bha- (2) "to speak, tell, say"). Meaning "quality of being shamefully vile" is from 1510s.
An earlier form in Middle English was infame (late 14c.), from Old French infame, an earlier form of infamie. Infame also was the Middle English verb in this set, "brand with infamy," from Old French infamer, from Latin infamare "bring into ill repute, defame," from infamis. The verb has become archaic in English (infamize is attested from 1590s).