We present UKIRT UIST spectra of Sakurai's Object (=V4334 Sgr) showing CO fundamental band absorption features around 4.7 microns. The line-centres are at heliocentric radial velocity of -170+/-30 km/s. The number and relative strengths of the lines indicate a CO gas temperature of 400+/-100 K and CO column density of 7(+3/-2)x10^17 per square cm. The gas was moving away from the central star at an average speed of 290+/-30 km/s in 2003 September. The lines appeared sometime between mid 1999 (well after the opaque dust shell formed) and mid 2000 and may have been somewhat more blue--shifted initially than they are now. The observed CO velocity and temperature indicate the continued presence of a fast wind in the object, previously seen in the He I 1.083 micron line beginning just prior to massive dust formation, and more recently in atomic and ionized lines. The dust continuum is consistent with a temperature of 350+/-30 K, indicating continued cooling of the shell. The similar CO temperature suggests that the bulk of the CO absorption occurs just outside of the dust continuum surface.