A self-wrapping, textile sleeve for routing and protecting elongate members from electromagnetic interference and a method of construction thereof is provided. The sleeve has an elongate wall constructed from interlaced yarns. At least one of the yarns is provided as heat-settable polymeric yarn that is heat-set to bias the wall into a self-wrapping configuration about a longitudinal central axis of the sleeve to bring opposite edges into overlapping relation with one another to provide a generally tubular cavity in which the elongate members are received. Further, at least one of the yarns is provided as a bi-component metallic wire having an aluminum core and an outer layer of copper.