An Etymological Dictionary of the German Language/Annotated/Muhme
Muhme, feminine (in Upper German almost obsolete), ‘aunt, female relative, nurse,’ from Middle High German muome, Old High German muoma, feminine, ‘mother's sister,’ also ‘sister-in-law, female relative.’ That the earlier meaning, ‘mother's sister’ (compare Base), is the originally one is shown by the connection of the word with Mutter. Old High German muoma points to Gothic *môna, as is indicated by Low German and Middle English mône, ‘aunt’ (for the change of n to m, see Pilgrim). The word is a pet form of or child's term for Anglo-Saxon môdrie, Low German mödder (equivalent to Welsh modryb, ‘aunt’), which have the same form as Greek μητρυΐα (compare Vetter with Vater); likewise Dutch moei from Middle Dutch moeie, ‘aunt.’ An old synonym occurs in Anglo-Saxon faþu, ‘aunt on the fathers side, father's sister,’ allied to Vater. Old Icelandic móna, ‘mother,’ and the equivalent Low German mœme, Lithuanian momà, Old Slovenian mama, seem to be pet terms for ‘mother’; so too Dutch moei, ‘aunt’ (Old High German muoia, Greek μαῖα).