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  km3. This analysis searches data taken on the partially completed detector during 2007 when roughly 0.2  km3 of ice was instrumented. The lack of candidate events leads to an upper limit on the flux of relativistic magnetic monopoles of Φ90%C.L.∼3×10−18  cm−2 sr−1 s−1 for β≥0.8. This is a factor of 4 improvement over the previous best experimental flux limits up to a Lorentz boost γ below 107. This result is then interpreted for a wide range of mass and kinetic energy values.