Many galactic and extragalactic astrophysical sources are currently considered promising candidates as high-energy neutrino emitters. Astrophysical neutrinos can be detected as upward-going muons produced in charged-current interactions with the medium surrounding the detector. The expected neutrino fluxes from various models start to dominate on the atmospheric neutrino background at neutrino energies above some tens of TeV. We present the results of a search for an excess of high-energy upward-going muons among the sample of data collected by MACRO during similar to5.8 years of effective running time. No significant evidence for this signal was found. As a consequence, an upper limit on the flux of upward-going muons from high-energy neutrinos was set at the level of 1.7 x 10(-14) cm(-2) s(-1) sr(-1). The corresponding upper limit for the diffuse neutrino flux was evaluated assuming a neutrino power law spectrum. Our result was compared with theoretical predictions and upper limits from other experiments. (C) 2002 Elsevier Science B.V. All rights reserved.