We search for pair-produced Dirac magnetic monopoles in 35.7 pb(-1) of proton-antiproton collisions at square root s = 1.96 TeV with the Collider Detector at Fermilab (CDF). We find no monopole candidates corresponding to a 95% confidence-level cross-section limit sigma < 0.2 pb for a monopole with mass between 200 and 700 GeV/c2. Assuming a Drell-Yan pair-production mechanism, we set a mass limit m > 360 GeV/c2.