The fungus Mycosphaerella graminicola has been a pathogen of wheat since host domestication 10,000-12,000 years ago in the Fertile Crescent. The wheat-infecting lineage emerged from closely related Mycosphaerella pathogens infecting wild grasses. We use a comparative genomics approach to assess how the process of host specialization affected the genome structure of M. graminicola since divergence from the closest known progenitor species named M. graminicola S1. The genome of S1 was obtained by Illumina sequencing resulting in a 35 Mb draft genome sequence of 32X. Assembled contigs were aligned to the previously sequenced M. graminicola genome. The alignment covered >90% of the non-repetitive portion of the M. graminicola genome with an average divergence of 7%. The sequenced M. graminicola strain is known to harbor thirteen essential chromosomes plus eight dispensable chromosomes. We found evidence that structural rearrangements significantly affected the dispensable chromosomes while the essential chromosomes were syntenic. At the nucleotide level, the essential and dispensable chromosomes have evolved differently. The average synonymous substitution rate in dispensable chromosomes is considerably lower than in essential chromosomes, whereas the average non-synonymous substitution rate is three times higher. Differences in molecular evolution can be related to different transmission and recombination patterns, as well as to differences in effective population sizes of essential and dispensable chromosomes. In order to identify genes potentially involved in host specialization or speciation, we calculated ratios of synonymous and non-synonymous substitution rates in the >9,500 aligned protein coding genes. The genes are generally under strong purifying selection. We identified 43 candidate genes showing evidence of positive selection, one encoding a potential pathogen effector protein. We conclude that divergence of these pathogens was accompanied by structural rearrangements in the small dispensable chromosomes, while footprints of positive selection were present in only a small number of protein coding genes.