The brain entropy (BEN) reflects the randomness of brain activity and is inversely related to its temporal coherence. In recent years, BEN has been found to be associated with a number of neurocognitive, biological, and sociodemographic variables such as fluid intelligence, age, sex, and education. However, evidence regarding the potential relationship between BEN and brain structure is still lacking. In this study, we use resting-state fMRI (rsfMRI) data to estimate BEN and investigate its associations with three structural brain metrics: gray matter volume (GMV), surface area (SA), and cortical thickness (CT). We performed separate analyses on BEN maps derived from four distinct rsfMRI runs, and used a voxelwise as well as a regions-of-interest (ROIs) approach. Our findings consistently showed that lower BEN was related to increased GMV and SA in the lateral frontal and temporal lobes, inferior parietal lobules, and precuneus. We hypothesize that lower BEN and higher SA might reflect higher brain reserve as well as increased information processing capacity.