From July 1987 through March 1988 an array of proportional wire modules was operated as a muon detector at a depth of 2090 meters water equivalent in the Soudan mine in northern Minnesota. A spatial angular resolution of 1.2°was achieved for muon tracking. A clean sample of 1.02×105 muon trajectories recorded underground is used to search for an excess flux of muons from the direction of Cygnus X-3. For muons within the phase interval [0.6, 0.9] of the source's 4.8-h period, 90%-C.L. upper limits for fluxes arriving within 3°and 1.5°half-angle cones centered on the Cygnus X-3 direction are 8.5×1011 cm-2s-1 and 3.1×10-11 cm-2s-1, respectively.