Myxoma virus (MYXV), endemic in Spain since 1952, is the causative agent of myxomatosis, a highly prevalent disease in European rabbits. In mid-2018, a myxomatosis outbreak was detected in the Iberian hare, a species indigenous to the Iberian Peninsula. MYXV isolated from infected Iberian hare tissues was identified as a novel recombinant MYXV strain, denominated ha-MYXV. This virus showed significant differences compared to the MYXV genome, highlighting a novel insert (Ins-H1) of 2.8 kb (containing M157L, M158L, M159L and M160L genes) that interrupts the M009 ORF. As an emerging virus occupying a novel ecological niche, the genetic stability of ha-MYXV is of particular interest. Therefore, the aim of this study was to monitor the Ins-H1 region using 106 lagomorph specimens, covering the eight-year period since its emergence, collected from 28 provinces across Spain. In addition, genomic analysis of several recent isolates was conducted using Oxford Nanopore Technologies. No mutations were detected in M157L or M158L and, in general, the M160L gene was highly conserved. M159 showed the most variation in the isolates analysed, demonstrating hypervariable microsatellite regions that may play a role in the evolution of ha-MYXV. The gene suffered alterations in the form of triplet nucleotide insertions and deletions, always maintaining the predicted ORF. It is interesting to speculate that the extensions and reductions in gene length may play a role in the adaptation of this virus to its novel host and may even facilitate further attempts to jump to closely related species. The identification of microsatellite regions within the M159 ORF led us to investigate the presence of further regions in the genome of ha-MYXV. The information provided by this study defines genome regions that may be targeted in future molecular epidemiological studies regarding ha-MYXV.