early 15c., "to cover or wrap (something) to conceal or protect," perhaps from Old French moufle "thick glove, mitten;" see muff (n.). Compare Old French enmoufle "wrapped up;" Middle French mofler "to stuff." The meaning "wrap something up to deaden sound" is recorded by 1761. Related: Muffled; muffling. Muffled oars have mats or canvas about their shafts to prevent noise from contact with the oarlocks while rowing.
"thing that muffles," 1560s, from muffle (v.). Originally "a muffler" (in the old sense), "a wrap for the lower face and neck." Meaning "a cover or wrap used to deaden sound" is by 1734.