We present the detection of carbon monoxide molecules (CO) at z = 1.6408 towards the quasar SDSS J160457.50+220300.5 using the Very Large Telescope Ultraviolet and Visual Echelle Spectrograph. We detected CO absorption in at least two components in the first six A-X bands and one d-X(5-0) interband system. This is the second detection of its kind along a quasar line of sight. The CO absorption profiles are well modelled by assuming rotational excitation of CO in the range 6 < T-ex < 16 K, which is consistent with or higher than the temperature of the cosmic microwave background radiation at this redshift. We derive a total CO column density of N(CO) = 4 x 10(14) cm(-2). The measured column densities of S I, Mg I, Zn II, Fe II, and Si II indicate a dust depletion pattern typical of cold gas in the Galactic disc. The background quasar spectrum is significantly reddened (u - K similar to 4.5 mag) and exhibits a pronounced 2175 angstrom dust absorption feature at the redshift of the CO absorber. Using a control sample of similar to 500 quasars, we find that the chance probability that this feature is spurious is similar to 0.3%. We show that the spectral energy distribution ( SED) of the quasar is well fitted by a QSO composite spectrum reddened with a Large Magellanic Cloud supershell extinction law at the redshift of the absorber. It is noticeable that this quasar is absent from the colour-selected SDSS quasar sample. This demonstrates that our current view of the Universe may be biased against dusty sightlines. These direct observations of carbonaceous molecules and dust open up the possibility of studying the physical conditions and chemistry of diffuse molecular gas in high redshift galaxies.