A sterile neutrino of ∼keV mass is a well-motivated dark matter candidate. Its decay generates an x-ray line that offers a unique target for x-ray telescopes. For the first time, we use the Gamma-ray Burst Monitor (GBM) onboard the Fermi Gamma-Ray Space Telescope to search for sterile neutrino decay lines; our analysis covers the energy range 10-25 keV (sterile neutrino mass 20-50 keV), which is inaccessible to x-ray and gamma-ray satellites such as Chandra, Suzaku, XMM-Newton, and INTEGRAL. The extremely wide field of view of the GBM enables a large fraction of the Milky Way dark matter halo to be probed. After implementing careful data cuts, we obtain ∼53 days of full-sky observational data. We observe an excess of photons towards the Galactic center, as expected from astrophysical emission. We search for sterile neutrino decay lines in the energy spectrum, and find no significant signal. From this, we obtain upper limits on the sterile neutrino mixing angle as a function of mass. In the sterile neutrino mass range 25-40 keV, we improve upon previous upper limits by approximately an order of magnitude. Better understanding of detector and astrophysical backgrounds, as well as detector response, will further improve the sensitivity of a search with the GBM.