The brighter-fatter (BF) effect is a phenomenon (originally discovered in charge coupled devices) in which the size of the detector point spread function (PSF) increases with brightness. We present, for the first time, laboratory measurements demonstrating the existence of the effect in a Hawaii-2RG HgCdTe near infrared (NIR) detector. We use the Precision Projector Laboratory, a JPL facility for emulating astronomical observations with UV/VIS/NIR detectors, to project about 17,000 point sources onto the detector to stimulate the effect. After calibrating the detector for nonlinearity with flat-fields, we find evidence that charge is nonlinearly shifted from bright pixels to neighboring pixels during exposures of point sources, consistent with the existence of a BF-type effect. The Wide Field Infrared Survey Telescope (WFIRST) by NASA will use similar detectors to measure weak gravitational lensing from the shapes of hundreds of million of galaxies in the NIR. The WFIRST PSF size must be calibrated to approximately 0.1 percent to avoid biased inferences of dark matter and dark energy parameters; therefore further study and calibration of the BF effect in realistic images will be crucial.