The Dark Energy Spectroscopic Instrument (DESI) will measure spectra of tens of millions of galaxies over the next few years with the primary goal of obtaining high-precision redshifts to study the expansion history of the universe. Galaxy velocity dispersions (σ) can also be obtained from these spectra, to probe galaxy formation histories as well as giving independent distance measurements. To determine how well σ can be recovered from the survey data, we perform fitting on spectra of 3441 galaxies taken at 1x and 3x the nominal DESI exposure time. After removing gas emission and sky lines, we find that σ is recovered consistently within measurement error for different spectra of the same galaxy. However, we also find that errors are systematically overestimated by the spectral fitting program. Finally, we show that σ as measured from the nominal exposure time gives a better prediction of a galaxy’s actual velocity dispersion than other properties such as color or bulge-disc ratio. We conclude that spectral fitting provides meaningful information about the velocity dispersions of the large populations of galaxies that DESI will observe and should be included in the future pipeline, although care should be taken to find spectral templates at resolutions matching the data.