A purpose is to provide a tubular body soundproof cover and a covered tubular body, for which elastic deformation of the tubular body is unlikely to be inhibited. The tubular body soundproof cover includes a sound absorbing layer arranged on outside in an axially perpendicular direction of a tubular body having tubular body side curved sections; a skin layer arranged on outside in the axially perpendicular direction of the sound absorbing layer; and cover side curved sections arranged on outside in the axially perpendicular direction of the tubular body side curved sections, including at least a portion of the sound absorbing layer and at least a portion of the skin layer. The cover side curved sections have non-adherent sections in which the sound absorbing layer and the skin layer are not bonded over the entire circumferential length.