We present here the draft genome sequences of multidrug-resistant blaNDM-1-positive Acinetobacter baumannii strains ACMH-6200 and ACMH-6201, isolated in north Lebanon from civilians wounded during the Syrian civil war. The draft genomes were contained in 217 contigs for ACMH-6200 and 83 contigs for ACMH-6201, including a combined 3,997,237 bases for ACMH-6200 and 3,983,110 bases for ACMH-6201, with 39% and 38.9% G+C content, respectively.