We present results of five Nuclear Spectroscopic Telescope Array (NuSTAR) observations of the type 2 active galactic nucleus (AGN) in IC 751, three of which were performed simultaneously with XMM-Newton or Swift/X-Ray Telescope. We find that the nuclear X-ray source underwent a clear transition from a Compton-thick (N-H similar or equal to 2 x 10(24) cm(-2)) to a Compton-thin (N-H similar or equal to 4 x 10(23) cm(-2)) state on timescales of less than or similar to 3 months, which makes IC 751 the first changing. look AGN discovered by NuSTAR. Changes of the line of sight column density at the similar to 2 sigma level are also found on a timescale of similar to 48 hr (Delta N-H similar to 10(23) cm(-2)). From the lack of spectral variability on timescales of similar to 100 ks, we infer that the varying absorber is located beyond the emission-weighted average radius of the broad-line region (BLR), and could therefore be related either to the external part of the BLR or a clumpy molecular torus. By adopting a physical torus X-ray spectral model, we are able to disentangle the column density of the non-varying absorber (N-H similar to 3.8 x 10(23) cm(-2)) from that of the varying clouds [N-H similar to (1 - 150) x 10(22) cm(-2)], and to constrain that of the material responsible for the reprocessed X-ray radiation (N-H similar to 6 x 10(24) cm(-2)). We find evidence of significant intrinsic X-ray variability, with the flux varying by a factor of five on timescales of a few months in the 2-10 and 10-50 keV band.