We report on the discovery of K2-141 b (EPIC 246393474 b), an ultra-short-period super-Earth on a 6.7-hour orbit transiting an active K7 V star based on data from K2 campaign 12. We confirmed the planet's existence and measured its mass with a series of follow-up observations: seeing-limited MuSCAT imaging, NESSI high-resolution speckle observations, and FIES and HARPS high-precision radial-velocity monitoring. K2-141 b has a mass of 5.31+/-0.46M_{Earth} and radius of 1.54+0.10-0.09R{Earth}, yielding a mean density of 8.00^+1.83^-1.45_g/cm^3^ and suggesting a rocky-iron composition. Models indicate that iron cannot exceed ~70% of the total mass. With an orbital period of only 6.7 hours, K2-141 b is the shortest-period planet known to date with a precisely determined mass.