Understanding the thermodynamics of Darwinian evolution has important implications for biophysics, evolutionary biology, and the study of the origin of life. We show that in a population of nonequilibrium autocatalytic replicators, the critical selection coefficient (i.e., the minimal fitness difference visible to selection) is lower bounded by the free energy dissipated per replication event. This bound represents a fundamental thermodynamic threshold for Darwinian evolution, analogous to selection thresholds that arise from finite population sizes or large mutation rates. Our results apply to a large class of molecular replicators, including many types of multistep autocatalytic reaction mechanisms and autocatalytic sets. We illustrate our approach on a thermodynamically-consistent model of simple replicators in a chemostat.