We computationally designed an ultranarrow-band wavelength-selective thermal radiator via a materials informatics method alternating between Bayesian optimization and thermal electromagnetic field calculation. For a given target infrared wavelength, the optimal structure was efficiently identified from over 8 billion candidates of multilayers consisting of multiple components (Si, Ge, and SiO2). The resulting optimized structure is an aperiodic multilayered metamaterial exhibiting high and sharp emissivity with a Q-factor of 273. The designed metamaterials were then fabricated, and reasonable experimental realization of the optimal performance was achieved with a Q-factor of 188, which is significantly higher than those of structures empirically designed and fabricated in the past. This is the first demonstration of the experimental realization of metamaterials designed by Bayesian optimization. The results facilitate the machine-learning-based design of metamaterials and advance our understanding of the narrow-band thermal emission mechanism of aperiodic multilayered metamaterials.