Because biochemical processes within individual cells involve a small number of molecules, they are subject to random fluctuations. As a result, isogenic cell populations show different concentrations of the same mRNA and protein, even in homogeneous conditions. The extent and consequences of this stochastic gene expression have only recently been assessed on a genome−wide scale, in particular thanks to the advent of single cell transcriptomics. Yet the evolutionary forces shaping this stochasticity remain to be unraveled. We took advantage of recently published data sets of the single cell transcriptome of the domestic mouse Mus musculus to characterize the genomic patterns of transcriptional stochasticity. We show that noise levels in the mRNA distributions (a.k.a. transcriptional noise) significantly correlate with nuclear domain organization, gene function and gene age. Position of the encoded protein in biological pathways, however, is the main factor that explains observed levels of transcriptional noise. We argue that these results are consistent with models of noise propagation within gene networks. Altogether, transcriptional noise appears to be under widespread selection and therefore constitutes an important of the phenotypical component. Differences in variance of expression – not only in mean expression level – potentially constitute a mechanism of adaptation and should be considered by functional and evolutionary studies of gene expression.