We study the electronic structure of the ferromagnetic spinel HgCr_{2}Se_{4} by soft-x-ray angle-resolved photoemission spectroscopy (SX-ARPES) and first-principles calculations. While a theoretical study has predicted that this material is a magnetic Weyl semimetal, SX-ARPES measurements give direct evidence for a semiconducting state in the ferromagnetic phase. Band calculations based on the density functional theory with hybrid functionals reproduce the experimentally determined band gap value, and the calculated band dispersion matches well with ARPES experiments. We conclude that the theoretical prediction of a Weyl semimetal state in HgCr_{2}Se_{4} underestimates the band gap, and this material is a ferromagnetic semiconductor.