The effect of hydrostatic pressure on the superconducting transition temperature of Na0.35CoO2.yH(2)O was investigated by ac susceptibility measurements up to 1.6 GPa. The pressure coefficient of T-c is negative and the dependence T-c(p) is nonlinear over the pressure range investigated. The magnitude of the average d ln T-c/dpapproximate to-0.07 GPa(-1) is comparable to the pressure coefficient of electron-doped high-T-c copper oxide superconductors with a similar value of T-c. Our results provide support to the assumption of two-dimensional superconductivity in Na0.35CoO2.yH(2)O, which is similar to the cuprate systems, and suggest that intercalation of larger molecules may lead to an enhancement of T-c.