This paper describes an experimental determination of the polarization of low-energy cosmic-ray μ mesons at sea level. A brass plate was placed in a horizontal position inside a magnetic solenoid. Particles which arrived from directions near the vertical and stopped in the plate were detected by a coincidence-anticoincidence counter telescope. Stopped negative μ mesons were destroyed by nuclear capture. Stopped positive μ mesons decayed into electrons which were detected by delayed coincidence counters placed above and below the plate. The upward and downward fluxes of the decay electrons leaving the absorber were measured alternately with and without a depolarizing magnetic field. The results of the measurements demonstrate that (1) cosmic-ray μ mesons are polarized, (2) the ratio between the downward fluxes of electrons from the decay of μ mesons stopped in a brass plate with and without a depolarizing magnetic field is 1.052+/-0.016, and (3) the indicated polarization of stopped positive μ mesons is 0.19+/-0.06 if the data are interpreted according to the two-component neutrino theory of μ-meson decay. The results are consistent with theoretical predictions based on the production spectrum of π mesons as found in other experiments.