Using an intense negative muon (μ^{-}) source, we have studied the internal magnetic fields in a powder sample of magnesium hydride (MgH_{2}). By extracting the signal from the μ^{-} captured on Mg nuclei, we found that the negative muon spin rotation and relaxation (μ^{-}SR) spectra clearly showed a Kubo-Toyabe-type relaxation, which indicates a random magnetic field at the Mg site. The field distribution width obtained is very consistent with the predicted value at the Mg site estimated by dipole field calculations, supporting our claim to have observed the nuclear magnetic fields of hydrogens in MgH_{2}. As is the case with μ^{+}SR, μ^{-}SR promises to soon be an indispensable tool for materials analyses.