K2-136 is a star in the Hyades with three known planets and an age of 790 ± 30 Myr. The planets (b, c, and d) have periods of 8.0, 17.3, 25.6 days and radii of 0.99 ± 0.05, 2.91 ± 0.11, and 1.45 ± 0.10 Earth radii, respectively. We collected radial velocity measurements with the HARPS-N spectrograph and found a semi-amplitude for planet c of 4.80 ± 0.73 m/s, from which we determined its mass to be 15.9 ± 2.4 Earth masses. We also placed 95% upper mass limits on planets b and d of 2.67 and 6.47 Earth masses, respectively. K2-136c is now the smallest planet to have a measured mass in an open cluster, as well as one of the youngest planets ever with a mass measurement. This research and future mass measurements of similar open cluster planets will shed light on the compositions and characteristics of small exoplanets at a very early stage of their lives and provide insights into how exoplanets evolve with time.