We report the draft genome assembly of Elizabethkingia meningoseptica strain 502. The sample was isolated from the wound of a repatriated military serviceperson who suffered major trauma from an improvised explosive device (IED), resulting in wounds with extensive environmental contamination. E. meningoseptica was isolated from wounds in both legs. The draft genome assembly has 21 contigs with a total size of 3,960,744 bases. The genome contains genes encoding 26 putative β-lactamases.