Multispectral photometric stereo (MPS) aims at recovering the surface normal of a scene from a single-shot multispectral image captured under multispectral illuminations. Existing MPS methods adopt the Lambertian reflectance model to make the problem tractable, but it greatly limits their application to real-world surfaces. In this paper, we propose a deep neural network named NeuralMPS to solve the MPS problem under non-Lambertian spectral reflectances. Specifically, we present a spectral reflectance decomposition model to disentangle the spectral reflectance into a geometric component and a spectral component. With this decomposition, we show that the MPS problem for surfaces with a uniform material is equivalent to the conventional photometric stereo (CPS) with unknown light intensities. In this way, NeuralMPS reduces the difficulty of the non-Lambertian MPS problem by leveraging the well-studied non-Lambertian CPS methods. Experiments on both synthetic and real-world scenes demonstrate the effectiveness of our method.