c. 1300, "tree of the genus Morus;" mid-14c. in reference to a berry from the tree; an alteration of morberie (13c.) from or cognate with Middle High German mul-beri (alteration by dissimilation of Old High German mur-beri, Modern German Maulbeere); both from Latin morum "mulberry, blackberry" + Old English berie, Old High German beri "berry."
The Latin word probably is from Greek moron "mulberry," from PIE *moro- "blackberry, mulberry" (source also of Armenian mor "blackberry," Middle Irish merenn, Welsh merwydden "mulberry"). As a color-name by 1837. The children's singing game with a chorus beginning "Here we go round the mulberry bush" is attested by 1820s, first in Scotland.