Results from the IceCube Neutrino Observatory have recently provided compelling evidence for the existence of a high energy astrophysical neutrino flux utilizing a dominantly Southern Hemisphere data set consisting primarily of ν(e) and ν(τ) charged-current and neutral-current (cascade) neutrino interactions. In the analysis presented here, a data sample of approximately 35,000 muon neutrinos from the Northern sky is extracted from data taken during 659.5 days of live time recorded between May 2010 and May 2012. While this sample is composed primarily of neutrinos produced by cosmic ray interactions in Earth's atmosphere, the highest energy events are inconsistent with a hypothesis of solely terrestrial origin at 3.7σ significance. These neutrinos can, however, be explained by an astrophysical flux per neutrino flavor at a level of Φ(E(ν))=9.9(-3.4)(+3.9)×10(-19) GeV(-1) cm(-2) sr(-1) s(-1)(E(ν)/100 TeV(-2), consistent with IceCube's Southern-Hemisphere-dominated result. Additionally, a fit for an astrophysical flux with an arbitrary spectral index is performed. We find a spectral index of 2.2(-0.2)(+0.2), which is also in good agreement with the Southern Hemisphere result.