Theory suggests that biological modularity and robustness allow for maintenance of fitness under mutational change, and when this change is adaptive, for evolvability. Empirical demonstrations that these traits promote evolvability in nature remain scant however. This is in part because modularity, robustness, and evolvability are difficult to define and measure in real biological systems. Here, we address whether structural modularity and/or robustness confer evolvability at the level of proteins by looking for associations between indices of protein structural modularity, structural robustness, and evolvability. We propose a novel index for protein structural modularity: the number of regular secondary structure elements (helices and strands) divided by the number of residues in the structure. We index protein evolvability as the proportion of sites with evidence of being under positive selection multiplied by the average rate of adaptive evolution at these sites, and we measure this as an average over a phylogeny of 25 mammalian species. We use contact density as an index of protein designability, and thus, structural robustness. We find that protein evolvability is positively associated with structural modularity as well as structural robustness and that the effect of structural modularity on evolvability is independent of the structural robustness index. We interpret these associations to be the result of reduced constraints on amino acid substitutions in highly modular and robust protein structures, which results in faster adaptation through natural selection.