Automated materials design with machine learning is increasingly common in recent years. Theoretically, it is characterized as black-box optimization in the space of candidate materials. Since the difficulty of this problem grows exponentially in the number of variables, designing complex materials is often beyond the ability of classical algorithms. We show how quantum annealing can be incorporated into automated materials discovery and conduct a proof-of-principle study on designing complex thermofunctional metamaterials. Our algorithm consists of three parts: regression for a target property by factorization machine, selection of candidate metamaterial based on the regression results, and simulation of the metamaterial property. To accelerate the selection part, we rely on the D-Wave 2000Q quantum annealer. Our method is used to design complex structures of wavelength selective radiators showing much better concordance with the thermal atmospheric transparency window in comparison to existing human-designed alternatives.