A nonwoven sleeve and method of construction thereof is provided, with the nonwoven sleeve having a tubular nonwoven wall bounding an inner cavity for receipt of an elongate member therein. The tubular nonwoven wall includes a strip of nonwoven material spiral wrapped about a central longitudinal axis of the wall, with opposite edges of the strip being brought into abutment with one another to form a spiral butt joint. The opposite edges of the nonwoven strip are bonded together across the butt joint by melted material of the strip. The nonwoven strip is bonded in tubular fashion along its length such that the nonwoven wall is not subject to unraveling and forming loose end pieces of the strip of nonwoven material.