Old English bannan "to summon, command, proclaim," from Proto-Germanic *bannan "to speak publicly" (used in reference to various sorts of proclamations), "command; summon; outlaw, forbid" (source also of Old Frisian bonna "to order, command, proclaim," Old High German bannan "to command or forbid under threat of punishment," German bannen "banish, expel, curse"), apparently a Germanic specialization from a suffixed form of PIE root *bha- (2) "to speak, tell, say" (source also of Old Irish bann "law," Armenian ban "word").
From mid-12c. as "to curse, condemn, pronounce a curse upon;" from late 14c. as "to prohibit;" these senses likely are via the Old Norse cognate banna "to curse, prohibit," and probably in part from Old French banir "to summon, banish" (see banish) and was a borrowing from Germanic. The sense evolution in Germanic was from "speak" to "proclaim a threat" to (in Norse, German, etc.) "to curse, anathematize."
The Germanic root, borrowed in Latin and French, has been productive: banal, bandit, contraband, etc. Related: Banned; banning. Banned in Boston dates from 1920s, in allusion to the excessive zeal and power of that city's Watch and Ward Society. Ban the bomb as a slogan of the nuclear disarmament movement is from 1955.
c. 1300, "proclamation or edict of an overlord," from Old English (ge)bann "proclamation, summons, command" and cognate Old French ban "decree, announcement," which is from a Germanic language, from Proto-Germanic *bannaz (source also of Old Frisian bon "order, commandment; jurisdiction, penalty; eternal damnation, excommunication," Old Saxon bann "commandment, prohibition"), from *bannan "to speak publicly" (used in reference to various sorts of proclamations), "command; summon; outlaw, forbid" (see ban (v.)). Meaning "an authoritative prohibition" is from 1660s. There are noun forms in most of the Germanic languages, from the verbs. Compare banns.