late 14c., mitain (from mid-13c. in surnames) "a glove, a covering for the hand," especially "a covering for the hand, differing from a glove in not having a separate covering for each finger, the thumb only being separated," from Old French mitaine "mitten, half-glove" (12c.) and from Medieval Latin mitta, both of uncertain origin; both perhaps from Middle High German mittemo, Old High German mittamo "middle, midmost" (reflecting the notion of "half-glove"), or from Vulgar Latin *medietana "divided in the middle," from Latin medius (see medial (adj.)).
From 1755 as "lace or knitted silk glove for women covering the forearm, the wrist, and part of the hand," worn fashionably by women in the early 19c. and revived towards the end of it. Hence get the mitten (1825), of men, "be refused or dismissed as a lover" (colloquial), from the notion of receiving the mitten instead of the "hand."