We present the first results in the search for relativistic magnetic monopoles with the IceCube detector, a subsurface neutrino telescope located in the South Polar ice cap containing a volume of 1 km^3. This analysis searches data taken on the partially completed detector during 2007 when roughly 0.2 km^3 of ice was instrumented. The lack of candidate events leads to an upper limit on the flux of relativistic magnetic monopoles of Փ_90%C.L. ~ 3 x 10^-18 cm^-2 sr^-1 s^-1 for �� ≥ 0.8. This is a factor of 4 improvement over the previous best experimental flux limits up to a Lorentz boost y below 10^7. This result is then interpreted for a wide range of mass and kinetic energy values.