Cytosine methylation is one of the most important epigenetic marks that regulate the process of gene expression. Here, we have examined the effect of epigenetic DNA methylation on nucleosomal stability using molecular dynamics simulations and elastic deformation models. We found that methylation of CpG steps destabilizes nucleosomes, especially when these are placed in sites where the DNA minor groove faces the histone core. The larger stiffness of methylated CpG steps is a crucial factor behind the decrease in nucleosome stability. Methylation changes the positioning and phasing of the nucleosomal DNA, altering the accessibility of DNA to regulatory proteins, and accordingly gene functionality. Our theoretical calculations highlight a simple physical-based explanation on the foundations of epigenetic signaling.