Invasive species introductions provide an ideal opportunity to study current evolution. Although the process of invasion has been shown to involve both random and adaptive genetic changes, it is rare to capture these changes while they are occurring. Further, few examples of selection on the mitochondrial genome in wild populations exist. Here we show that, in a recent invasion, there were rapid directed changes in mitochondrial DNA genotype proportions, with two genotypes found in heteroplasmic states. We considered processes of admixture, selection and random drift at both the population level and in the gametogenic tissue. We show that the observed changes are best explained by selective replication of mitochondria carrying newly-arisen genotypes at the advancing front.  Our finding of current selection on mitochondrial DNA, which is often postulated as a constraint for phylogenetic analyses, is rarely seen in action and is important to understanding adaption in invasive populations.