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 $10.6\pm 3.0ms-1$, which matches the transit ephemeris, and translates to a planet mass of $21.8\pm 6.2M\oplus$. 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, $2.04-0.61+0.66gcm-3$, implies that K2-100b retains a significant volatile envelope. We estimate that the planet is losing its atmosphere at a rate of $1011-1012gs-1$ due to the high level of radiation it receives from its host star.