ban (v.) Look up ban at Dictionary.com
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 banna "command, proclaim," Old High German bannan "to command or forbid under threat of punishment," German bannen "banish, expel, curse"), from 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.
ban (n.1) Look up ban at Dictionary.com
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 *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.
ban (n.2) Look up ban at Dictionary.com
1610s, "Croatian military chief," a title given to those who governed and guarded the southern marches of Hungary, later to the Austrian-appointed governors of Croatia and Slovenia, from Serbo-Croatian ban "lord, master, ruler," from Persian ban "prince, lord, chief, governor," which is cognate with Sanskrit pati "guards, protects." Hence banat "district governed by a ban," with Latinate suffix -atus. The Persian word is said to have gotten into Slavic via the Avars.