At wavelengths longwards of the sensitivity of silicon, hybrid structured mercury–cadmium–telluride (HgCdTe) detectors show promise to enable extremely precise radial velocity (RV) measurements of late-type stars. The most advanced near-infrared (NIR) detector commercially available is the HAWAII series (HxRG) of NIR detectors. While the quantum efficiency of such devices has been shown to be ≈90  %  , the noise characteristics of these devices, and how they relate to RV measurements, have yet to be quantified. We characterize the various noise sources generated by H4RG arrays using numerical simulations. We present recent results using our end-to-end spectrograph simulator in combination with the HxRG Noise Generator, which emulates the effects of read noise, parameterized by white noise, correlated and uncorrelated pink (1  /  f) noise, alternating column noise, and picture frame noise. The effects of nonlinear pixel response, dark current, persistence, and interpixel capacitance on RV precision are also considered. Our results have implications for RV error budgets and instrument noise floors that can be achieved with NIR Doppler spectrographs that utilize this kind of detector.