The LDA+DMFT (local density approximation combined with dynamical mean-field theory) computation scheme has been used to study spectral and magnetic properties of FeSi and Fe1−xCoxSi. Having compared different models, we conclude that a correlated band insulator scenario in contrast to Kondo insulator model agrees well with FeSi band structure and experimental data. Coulomb correlation effects lead to band narrowing of the states near the Fermi level with mass renormalization parameter m∗≈2 in agreement with the results of angle-resolved photoemission spectroscopy. Temperature dependence of spectral functions and magnetic susceptibility calculated in DMFT reproduces transition from nonmagnetic semiconductor to metal with local magnetic moments observed experimentally. Cobalt doping leads to ferromagnetism that has itinerant nature and can be successfully described by the LDA+DMFT method.