A wrappable textile tubular sleeve for routing and protecting elongate members is provided. The sleeve includes an elongate wall constructed from interlaced yarns. The wall has opposite inner and outer edges extending between opposite ends of the sleeve parallel to a central longitudinal axis of the sleeve. The wall also has oppositely facing inner and outer faces extending between the inner and outer edges. The inner face bounds an inner cavity of the tubular sleeve upon wrapping the outer edge in outwardly overlapping relation with the inner edge about the central longitudinal axis. Further, an elongate fastener extends parallel to the central longitudinal axis adjacent the outer edge. The fastener faces outwardly from the outer face and is configured for attachment to an external support member.