We report simultaneous multicolor near-infrared (NIR) observations of the supernova associated with X-ray flash 060218 during the first 16 days after the high-energy event. We find that the light curve rises and peaks relatively fast compared to other Type Ic supernovae (SNe Ic), with the characteristic broad NIR peak seen in all three bands. We find that the rise profile before the peak is largely independent of NIR wavelength, each band appearing to transition into a plateau phase around day 10-13. Since the light curve is in the plateau phase when our observations end at day 16, we can only place limits on the peak absolute magnitudes, but we estimate that SN 2006aj is one of the lowest NIR luminosity X-ray flash/gamma-ray burst (XRF/GRB) associated SNe observed to date. The broad peaks observed in the JHK