The first results from the Cryogenic Dark Matter Search for weakly interacting massive particles (WIMP) in the Soudan Underground Laboratory, were investigated. Four Ge and two Si detectors were operated for about 52.6 live days, which provided 19.4 kg d of Ge net exposure after cuts for recoil energies of range between 10 and 100 keV. To define the energy threshold and selection criteria for nuclear-recoil candidates, a blind analysis was performed. These data set the world's lowest exclusion limits on the coherent WIMP-nucleon scalar cross section for all WIMP masses above 15 GeV/c 2. The results show that the minimum of this limit at the 90% C.L. is 4×10-43 cm2 at a WIMP mass of 60 GeV/c 2.