M87 hosts a 3-6 billion solar mass black hole with a remarkable relativistic jet that has been regularly monitored in radio to TeV bands. However, hard X-ray emission. greater than or similar to 10 keV, which would be expected to primarily come from the jet or the accretion flow, had never been detected from its unresolved X-ray core. We report NuSTAR detection up to 40 keV from the the central regions of M87. Together with simultaneous Chandra observations, we have constrained the dominant hard X-ray emission to be from its unresolved X-ray core, presumably in its quiescent state. The core spectrum is well fitted by a power law with photon index Gamma = 2.11(-0.11)(+0.15) . The measured flux density at 40 keV is consistent with a jet origin, although emission from the advection-dominated accretion flow cannot be completely ruled out. The detected hard X-ray emission is significantly lower than that predicted by synchrotron self-Compton models introduced to explain emission above a GeV.