The IceCube Neutrino Observatory is a 1 km(3) detector currently taking data at the South Pole. One of the main strategies used to look for astrophysical neutrinos with IceCube is the search for a diffuse flux of high-energy neutrinos from unresolved sources. A hard energy spectrum of neutrinos from isotropically distributed astrophysical sources could manifest itself as a detectable signal that may be differentiated from the atmospheric neutrino background by spectral measurement. This analysis uses data from the IceCube detector collected in its half completed configuration which operated between April 2008 and May 2009 to search for a diffuse flux of astrophysical muon neutrinos. A total of 12 877 upward-going candidate neutrino events have been selected for this analysis. No evidence for a diffuse flux of astrophysical muon neutrinos was found in the data set leading to a 90% C. L. upper limit on the normalization of an E-2 astrophysical nu(mu) flux of 8.9 x 10(-9) GeV cm(-2) s(-1) sr(-1). The analysis is sensitive in the energy range between 35 TeV and 7 PeV. The 12 877 candidate neutrino events are consistent with atmospheric muon neutrinos measured from 332 GeV to 84 TeV and no evidence for a prompt component to the atmospheric neutrino spectrum is found.