We report on Landau-level spectroscopy of an epitaxially grown thin film of the topological insulator Sb2Te3, complemented by ellipsometry and magnetotransport measurements. The observed response suggests that Sb2Te3 is a direct-gap semiconductor with the fundamental band gap located at the Γ point or along the trigonal axis, and its width reaches Eg=(190±10) meV at low temperatures. Our data also indicate the presence of other low-energy extrema with a higher multiplicity in both the conduction and valence bands. The conclusions based on our experimental data are confronted with and to a great extent corroborated by the electronic band structure calculated using the GW method.