In many species, meiotic recombination is concentrated in small genomic regions. These “recombination hotspots” leave signatures in fine-scale patterns of linkage disequilibrium, raising the prospect that the genomic landscape of hotspots can be characterized from sequence variation. This approach has led to the inference that recombination hotspots evolve rapidly in some species, but are conserved in others. Historic demographic events, such as population bottlenecks, are known to affect patterns of linkage disequilibrium across the genome, violating population genetic assumptions of this approach. Such events are prevalent, yet demographic history is generally unaccounted for when making inferences about the evolution of recombination hotspots. To determine the effect of demography on the detection of recombination hotspots, we use the coalescent to simulate haplotypes with a known recombination landscape. We measure the ability of popular linkage disequilibrium-based programs to detect recombination hotspots under different demographic histories, including population bottlenecks, hidden population structure, population expansions and population contractions. We find that demographic events, and in particular, population bottlenecks and exponential population growth, have the potential to greatly reduce the power to discover recombination hotspots, in some cases by up to 90%. Furthermore, demographic events also have the potential to increase the false positive rate of hotspot discovery. In the worst-case scenario, long, slow population contractions quadruple the frequency of false positives, even under stringent significance cutoffs. We tested whether simple genomic parameters, such as nucleotide diversity or heterozygosity, could be used to predict the reduction in power due to non-equilibrium demographic histories. We found that neither the power, nor the false positive rate, of hotspot detection could be predicted without also knowing the demographic history of the sample. Our results suggest that ignoring demographic history likely overestimates the power to detect recombination hotspots and underestimates the degree to which recombination hotspots are shared between closely related species. We make specific recommendations for how demographic inference can be incorporated into population genetic inferences about recombination hotspots.