Probabilistic methods for model updating based on Bayesian inference are becoming standard in engineering, since they provide accurate predictions of parameters and their associated uncertainty. Furthermore, Bayesian inference provides a framework for model class selection, so different parametric models can be associated with a measure of plausibility based on the available data. Despite these important characteristics, it is still challenging the definition of a parametric form for a model class, since the construction of such functional form can be a complex problem involving a thorough understanding of the physical phenomenon being addressed. To overcome this problem, a novel nonparametric method for model updating and model class selection based on General Regression Neural Network (GRNN) and Bayesian inference is proposed. The proposed method, denominated Bayesian Nonparametric General Regression (BNGR), is appealing since it provides estimates of quantities of interest based on the available data without the specification of a functional form. Moreover, even though there is not a parametric form involved in the proposed methodology, the possibility for model class selection is kept. In this case a model class is defined as a set of design variables, so unrelated variables to the input-output relationship are discarded.