late 14c., "want of self-restraint, misbehavior" (a sense now obsolete), from mis- (1) "badly, wrongly" + government. Meaning "bad government, management, or administration of public or private affairs" is from 1590s.
prefix of Germanic origin affixed to nouns and verbs and meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (source also of 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 possibly from PIE *mit-to-, from root *mei- (1) "to change."
Productive 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 it came to be used as an intensive prefix with words 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.). It has become confused with mis- (2).
late 14c., "act of governing or ruling;" 1550s, "system by which a thing is governed" (especially a state), from Old French governement "control, direction, administration" (Modern French gouvernement), from governer "to steer, be at the helm of; govern, rule, command, direct," from Latin gubernare "to direct, rule, guide, govern," originally "to steer, to pilot"(see govern). Meaning "governing power" in a given place is from 1702. Compare governance.
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Harper, D. (n.d.). Etymology of misgovernment. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/misgovernment