We present a detailed analysis of HARPS-N radial velocity observations of K2-100, a young and active star in the Praesepe cluster, which hosts a transiting planet with a period of 1.7 days. We model the activity-induced radial velocity variations of the host star with a multi-dimensional Gaussian Process framework and detect a planetary signal of \(10.6 \pm 3.0 {\rm m\,s^{-1}}\), which matches the transit ephemeris, and translates to a planet mass of \(21.8 \pm 6.2 M_\oplus\). We perform a suite of validation tests to confirm that our detected signal is genuine. This is the first mass measurement for a transiting planet in a young open cluster. The relatively low density of the planet, \(2.04^{+0.66}_{-0.61} {\rm g\,cm^{-3}}\), implies that K2-100b retains a significant volatile envelope. We estimate that the planet is losing its atmosphere at a rate of \(10^{11}-10^{12}\,{\rm g\,s^{-1}}\) due to the high level of radiation it receives from its host star.