We present a hard X-ray Nuclear Spectroscopic Telescope Array (NuSTAR) observation of PSR J0437-4715, the nearest millisecond pulsar. The known pulsations at the apparent pulse period similar to 5.76 ms are observed with a significance of 3.7 sigma, at energies up to 20 keV above which the NuSTAR background dominates. We measure a photon index Gamma = 1.50 +/- 0.25 (90 per cent confidence) for the power-law fit to the non-thermal emission. It had been shown that spectral models with two or three thermal components fit the XMM-Newton spectrum of PSR J0437-4715, depending on the slope of the power-law component, and the amount of absorption of soft X-rays. The new constraint on the high-energy emission provided by NuSTAR removes ambiguities regarding the thermal components of the emission below 3 keV. We performed a simultaneous spectral analysis of the XMM-Newton and NuSTAR data to confirm that three thermal components and a power law are required to fit the 0.3-20 keV emission of PSR J0437-4715. Adding a ROSAT-PSPC spectrum further confirmed this result and allowed us to better constrain the temperatures of the three thermal components. A phase-resolved analysis of the NuSTAR data revealed no significant change in the photon index of the high-energy emission. This NuSTAR observation provides further impetus for future observations with the NICER mission (Neutron Star Interior Composition Explorer) whose sensitivity will provide much stricter constraints on the equation of state of nuclear matter by combining model fits to the pulsar's phase-folded light curve with the pulsar's well-defined mass and distance from radio timing observations.