Natural killer (NK) cells express inhibiting receptors (iNKRs), which specifically bind MHC-I molecules on the surface of healthy cells. When the expression of MHC-I on the cell surface decreases, which might occur during certain viral infections and cancer, iNKRs lose inhibiting signals and the infected cells become target for NK cell activation (missing-self detection). Although the detection of MHC-I deficient cells can be achieved by conserved receptor-ligand interactions, several iNKRs are encoded by gene families with a remarkable genetic diversity, containing many haplotypes varying in gene content and allelic polymorphism. So far, the biological function of this expansion within the NKR cluster has remained poorly understood. Here, we investigate whether the evolution of diverse iNKRs genes can be driven by a specific viral immunoevasive mechanism: selective MHC downregulation. Several viruses, including EBV, CMV, and HIV, decrease the expression of MHC-I to escape from T cell responses. This downregulation does not always affect all MHC loci in the same way, as viruses target particular MHC molecules. To study the selection pressure of selective MHC downregulation on iNKRs, we have developed an agent-based model simulating an evolutionary scenario of hosts infected with herpes-like viruses, which are able to selectively downregulate the expression of MHC-I molecules on the cell surface. We show that iNKRs evolve specificity and, depending on the similarity of MHC alleles within each locus and the differences between the loci, they can specialize to a particular MHC-I locus. The easier it is to classify an MHC allele to its locus, the lower the required diversity of the NKRs. Thus, the diversification of the iNKR cluster depends on the locus specific MHC structure.