"bind with long strips of cloth," late 15c. alteration of Middle English swathlen (c. 1200), probably a frequentative form of Old English swaþian (see swathe). Related: Swaddled; swaddling. Phrase swaddling clothes is from Coverdale (1535) translation of Luke ii.7.
Young children ... are still bandaged in this manner in many parts of Europe to prevent them from using their limbs freely, owing to a fancy that those who are left free in infancy become deformed. [Century Dictionary, 1891]
Wyclif uses swathing-clothes (late 14c.).