We present an analysis of NuSTAR X-ray observations in the 3-79 keV energy band of the Seyfert 2 galaxy NGC 4388, taken in 2013. The broadband sensitivity of NuSTAR, covering the Fe K alpha line and Compton reflection hump, enables tight constraints to be placed on reflection features in AGN X-ray spectra, thereby providing insight into the geometry of the circumnuclear material. In this observation, we found the X-ray spectrum of NGC 4388 to be well described by a moderately absorbed power law with non-relativistic reflection. We fit the spectrum with phenomenological reflection models and a physical torus model. and find the source to be absorbed by Compton-thin material (N-H = (6.5 +/- 0.8) x 10(23) cm(-2)) with a very weak Compton reflection hump (R < 0.09) and an exceptionally large Fe K alpha line (EW = 368(-53)(+56) eV) for a source with weak or no reflection. Calculations using a thin-shell approximation for the expected Fe K alpha EW indicate that an Fe K alpha line originating from Compton-thin material presents a possible explanation.