We present joint theoretical-experimental study of correlation effects in the electronic structure of (pyH)3[Mn4O3Cl7(OAc)3]⋅2MeCN molecular magnet (Mn4). Describing the many-body effects by cluster dynamical mean-field theory, we find that Mn4 is predominantly a Hubbard insulator with strong electron correlations. The calculated electron gap (1.8eV) agrees well with the results of optical conductivity measurements, while other methods, which neglect many-body effects or treat them in a simplified manner, do not provide such an agreement. Strong electron correlations in Mn4 may have important implications for possible future applications.