We present infrared (IR) absorption spectra of cryogenic parahydrogen solids doped with small water clusters. We observe a sequence of peaks shifted to the red by approximate to 15 cm(-1) from the absorptions of cyclic water clusters in liquid helium droplets [K. Nauta and R. E. Miller, Science 287, 293 (2000)]; this sequence includes the peak due to the cyclic isomer of the water hexamer: cyc-(H2O)(6). We believe this is only the second spectroscopic observation of isolated cyc-(H2O)(6), and the first report of the IR spectrum of the isolated cluster in the solid phase.