A total of 614 upward throughgoing muons of minimum energy 1.6 GeV are observed by Super-Kamiokande during 537 detector live days. The measured muon flux is [1.74 +/- 0.07(stat) +/- 0.02(sys)] x 10(-13) cm(-2) s(-1) sr(-1) compared to an expected flux of [1.97 +/- 0.44(theor)] x 10(-13) cm(-2) s(-1) sr(-1). The absolute measured flux is in agreement with the prediction within the errors. However, the zenith-angle dependence of the observed upward throughgoing muon flux does not agree with no-oscillation predictions. The observed distortion in shape is consistent with the nu(mu) <-> nu(tau) oscillation hypothesis with sin(2) 2 theta > 0.4 and 1 x 10(-3) < Delta m(2) < 1 x 10(-1) eV(2) at 90% confidence level. [S0031-9007(99)08762-1].