Longman Dictionary of Contemporary English
The Collaborative International Dictionary
Mis- \Mis-\ (m[i^]s-). [In words of Teutonic origin, fr. AS. mis-; akin to D. mis-, G. miss-, OHG. missa-, missi-, Icel. & Dan. mis-, Sw. miss-, Goth. missa-; orig., a p. p. from the root of G. meiden to shun, OHG. m[=i]dan, AS. m[=i][eth]an ([root]100. Cf. Miss to fail of). In words from the French, fr. OF. mes-, F. m['e]-, mes-, fr. L. minus less (see Minus). In present usage these two prefixes are commonly confounded.] A prefix used adjectively and adverbially in the sense of amiss, wrong, ill, wrongly, unsuitably; as, misdeed, mislead, mischief, miscreant.
Douglas Harper's Etymology Dictionary
prefix meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (cognates: Old Frisian and Old Saxon mis-, Middle Dutch misse-, Old High German missa-, German miß-, Old Norse mis-, Gothic missa-), perhaps literally "in a changed manner," and with a root sense of "difference, change" (compare Gothic misso "mutually"), and thus from PIE *mit-to-, from root *mei- (1) "to change" (see mutable); see Watkins.\n
\nOthers [Barnhart] see in Proto-Germanic *missa- the stem of an ancient past participle, related to Old English missan "fail to hit" (see miss (v.)), which is from the same PIE root.\n
\nProductive as word-forming element in Old English (as in mislæran "to give bad advice, teach amiss"). In 14c.-16c. in a few verbs its sense began to be felt as "unfavorably" and was used as an intensive prefix with verbs already expressing negative feeling (as in misdoubt). Practically a separate word in Old and early Middle English (and often written as such). Old English also had an adjective (mislic "diverse, unlike, various") and an adverb (mislice "in various directions, wrongly, astray") derived from it, corresponding to German misslich (adj.).
pre. 1 bad, badly, wrong, wrongly 2 lack or failure