Rensch's rule refers to a pattern in sexual size dimorphism (SSD) in which SSD decreases with body size when females are the larger sex and increases with body size when males are the larger sex. Many animal taxa conform to Rensch's rule, but it has yet to be investigated in plants. Using herbarium collections from New Zealand, we characterized the size of leaves and stems of 297 individuals from 38 dioecious plant species belonging to three distantly related phylogenetic lineages. Statistical comparisons of leaf sizes between males and females showed evidence for Rensch's rule in two of the three lineages, indicating SSD decreases with leaf size when females produce larger leaves and increases with leaf size when males produce larger leaves. A similar pattern in SSD was observed for stem sizes. However, in this instance, females of small-stemmed species produced much larger stems than did males, but as stem sizes increased, SSD often disappeared. We hypothesize that sexual dimorphism in stem sizes results from selection for larger stems in females, which must provide mechanical support for seeds, fruits, and dispersal vectors, and that scaling relationships in leaf sizes result from correlated evolution with stem sizes. The overall results suggest that selection for larger female stem sizes to support the weight of offspring can give rise to Rensch's rule in dioecious plants.