Mid 19th century; earliest use found in Daniel Wilson (1816–1892), anthropologist and university administrator. From classical Latin monoxylus or its etymon ancient Greek μονόξυλος + -ic, after monoxyle, monoxylon.
xylophone from mid 19th century:
This is the only common word formed from Greek xylo- ‘wood’, although it is common enough in science in words such as xylene (mid 19th century) a hydrocarbon made from distilled wood, and archaeologists can describe a single lump of wood as monoxylic (mid 19th century) on the model of monolithic (mid 19th century) for ‘single stone’.