  We present a temperature-dependent infrared spectroscopy study on the layered
topological semimetal Nb$_3$SiTe$_6$ combined with density-functional theory
(DFT) calculations of the electronic band structure and optical conductivity.
Our results reveal an anisotropic behavior of the in-plane ($ac$-plane) optical
conductivity, with three pronounced excitations located at around 0.15, 0.28,
and 0.41~eV for the polarization of the incident radiation along the $c$ axis.
These excitations are well reproduced in the theoretical spectra. Based on the
\textit{ab initio} results, the excitations around 0.15 eV and 0.28 eV are
interpreted as fingerprints of van Hove singularities in the electronic band
structure and compared to the findings for other topological semimetals.
