This Letter reports results from the MINOS experiment based on its initial exposure to neutrinos from the Fermilab NuMI beam. The rates and energy spectra of charged current nu(mu) interactions are compared in two detectors located along the beam axis at distances of 1 and 735 km. With 1.27 x 10(20) 120 GeV protons incident on the NuMI target, 215 events with energies below 30 GeV are observed at the Far Detector, compared to an expectation of 336+/-14 events. The data are consistent with nu(mu) disappearance via oscillations with |Delta(m)2/32|=2.74 +0.44/-0.26 x10(-3)eV(2) and sin(2)(2theta(23))>0.87 (68% C.L.).