We tested the hypothesis that the rate of marsupial cranial evolution is dependent on the distribution of genetic variation in multivariate space. To do so, we carried out a genetic analysis of cranial morphological variation in laboratory strains of Monodelphis domestica and used estimates of genetic covariation to analyse the morphological diversification of the Monodelphis brevicaudata species group. We found that within-species genetic variation is concentrated in only a few axes of the morphospace and that this strong genetic covariation influenced the rate of morphological diversification of the brevicaudata group, with between-species divergence occurring fastest when occurring along the genetic line of least resistance. Accounting for the geometric distribution of genetic variation also increased our ability to detect the selective regimen underlying species diversification, with several instances of selection only being detected when genetic covariances were taken into account. Therefore, this work directly links patterns of genetic covariation among traits to macroevolutionary patterns of morphological divergence. Our findings also suggest that the limited distribution of Monodelphis species in morphospace is the result of a complex interplay between the limited dimensionality of available genetic variation and strong stabilizing selection along two major axes of genetic variation.