A challenging problem in the classification of daily solar radiation is the selection of the appropriate model complexity and size that best describe the data. This paper introduces a new nonparametric Bayesian method for automatic classification of daily clearness index, by assuming Dirichlet process as a nonparametric prior on the model parameters. Nonparametric methods are free from the parametric model assumptions, and there is no need to specify any parametric specifications, or to restrict the number of classes. Our approach relies on the inference of the posterior distributions using the collapsed Gibbs sampler. The proposed method is tested using measurements from 2003 to 2016, at the Silver Lake monitoring station in the USA (121 degrees 3'W, 43 degrees 7'N), with a 5 min logging interval. By applying our classification algorithm, three classes of daily clearness index distributions are identified, corresponding to three types of sky cloudiness, namely cloudy, partially cloudy, and clear sky. The proposed classification framework can facilitate the design of solar radiation conversion systems.