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 \Phi _ { \mathrm { 90 \%C . L . } } \sim 3 \times 10 ^ { -18 } \mathrm { cm ^ { -2 } sr ^ { -1 } s ^ { -1 } } for \beta \geq 0.8 . This is a factor of 4 improvement over the previous best experimental flux limits up to a Lorentz boost \gamma below 10 ^ { 7 } . This result is then interpreted for a wide range of mass and kinetic energy values .