Recent laboratory experiments suggest that a molecule's ability to evolve neutrally is important for its ability to generate evolutionary innovations. In contrast to laboratory experiments, life unfolds on time-scales of billions of years. Here, we ask whether a molecule's ability to evolve neutrally-a measure of its robustness-facilitates evolutionary innovation also on these large time-scales. To this end, we use protein designability, the number of sequences that can adopt a given protein structure, as an estimate of the structure's ability to evolve neutrally. Based on two complementary measures of functional diversity-catalytic diversity and molecular functional diversity in gene ontology-we show that more robust proteins have a greater capacity to produce functional innovations. Significant associations among structural designability, folding rate and intrinsic disorder also exist, underlining the complex relationship of the structural factors that affect protein evolution.