A woven sleeve and method of construction thereof is provided. The sleeve has a wall with opposite edges extending lengthwise along a longitudinal axis between opposite ends, wherein the opposite edges are wrappable into overlapping relation with one another to contain the wires within a cavity of the sleeve. The wall is constructed from warp yarns extending along the longitudinal axis and fill yarns extending transversely to the warp yarns. The fill yarns are provided as transparent or substantially transparent monofilaments and the warp yarns are provided as yarns including a multifilament yarn and at least one conductive wire, wherein the conductive wire wrapped about the multifilament yarn.