The McDonald-Kreitman (MK) test, which compares the ratio of polymorphism to divergence at nonsynonymous and synonymous sites, is frequently used to detect adaptive evolution in protein-coding sequences. Because the two classes of sites share a common evolutionary history, the MK test is thought to be robust to most demographic factors. However, weak selection on nonsynonymous sites can bias the MK test, especially when a species' effective population size has not been constant. Here, we present an empirical analysis of the influence of demography on the MK test by comparing test results for a common set of 136 genes, including a set of sex-biased genes that shows a strong signal of adaptive evolution, in two Drosophila melanogaster populations: an ancestral population from Africa and a derived population from Europe. The latter has undergone a relatively recent bottleneck, which has reduced its effective population size. We find that the MK test has less power to detect positive selection in the European population for two reasons. First, the overall reduced level of standing variation decreases the statistical power of the test. Second, the segregation of slightly deleterious nonsynonymous mutations biases the MK test away from detecting positive selection. The latter effect is stronger for X-linked genes, which have experienced the greatest reduction in effective population size outside of Africa, and also leads to the underestimation of rates of adaptive protein evolution by multilocus implementations of the MK test. Interestingly, a subset of autosomal female-biased genes shows an increased signal of adaptive evolution in the European population. This is inconsistent with currently accepted demographic scenarios and may reflect female-specific changes in selective constraint following the colonization of non-African habitats.