We present near-infrared spectroscopy of the NGC 5128 supernova SN 2016adj in the first 2 months following discovery. We report the detection of first overtone carbon monoxide emission at ~58.2 d after discovery, one of the earliest detections of CO in an erupting supernova. We model the CO emission to derive the CO mass, temperature and velocity, assuming both pure 12CO and a composition that includes 13CO; the case for the latter is the isotopic analyses of meteoritic grains, which suggest that core collapse supernovae can synthesise significant amounts of 13C. Our models show that, while the CO data are adequately explained by pure 12CO, they do not preclude the presence of 13CO, to a limit of 12C/13C>3, the first constraint on the 12C/13C ratio determined from near-infrared observations. We estimate the reddening to the object, and the effective temperature from the energy distribution at outburst. We discuss whether the ejecta of SN 2016adj may be carbon-rich, what the infrared data tell us about the classification of this supernova, and what implications the early formation of CO in supernovae may have for CO formation in supernovae in general.