We present a measurement of the flux of neutrino-induced upgoing muons (<Eν>~ 100 GeV) using the MACRO detector. The ratio of the number of observed to expected events integrated over all zenith angles is 0.74 +/-0.036 (stat) +/-0.046 (systematic) +/-0.13 (theoretical). The observed zenith distribution for -1.0<=cosθ<=-0.1 does not fit well with the no oscillation expectation, giving a maximum probability for χ2 of 0.1%. The acceptance of the detector has been extensively studied using downgoing muons, independent analyses and Monte Carlo simulations. The other systematic uncertainties cannot be the source of the discrepancies between the data and expectations. We have investigated whether the observed number of events and the shape of the zenith distribution can be explained by a neutrino oscillation hypothesis. Fitting either the flux or zenith distribution independently yields mixing parameters of sin22θ=1.0 and ∆m2 of a few times 10-3 eV2. However, the observed zenith distribution does not fit well with any expectations, giving a maximum probability for χ2 of 5% for the best oscillation hypothesis, and the combined probability for the shape and number of events is 17%. We conclude that these data favor a neutrino oscillation hypothesis, but with unexplained structure in the zenith distribution not easily explained by either the statistics or systematics of the experiment.