The 5.4 kton MINOS far detector has been taking charge-separated cosmic ray muon data since the beginning of August, 2003 at a depth of 207 m.w.e. in the Soudan Underground Laboratory, Minnesota, USA. The data with both forward and reversed magnetic field running configurations were combined to minimize systematic errors in the determination of the underground muon charge ratio. When averaged, two independent analyses find the charge ratio underground to be Nμ+/Nμ-=1.374±0.004(stat)-0.010+0.012(sys). Using the map of the Soudan rock overburden, the muon momenta as measured underground were projected to the corresponding values at the surface in the energy range 1-7 TeV. Within this range of energies at the surface, the MINOS data are consistent with the charge ratio being energy independent at the 2 standard deviation level. When the MINOS results are compared with measurements at lower energies, a clear rise in the charge ratio in the energy range 0.3-1.0 TeV is apparent. A qualitative model shows that the rise is consistent with an increasing contribution of kaon decays to the muon charge ratio. © 2007 The American Physical Society.