UV-induced photodesorption of ice is a non-thermal evaporation process that can explain the presence of cold molecular gas in a range of interstellar regions. Information on the average UV photodesorption yield of astrophysically important ices exists for broadband UV lamp experiments. UV fields around low-mass pre-main-sequence stars, around shocks and in many other astrophysical environments are however often dominated by discrete atomic and molecular emission lines. It is therefore crucial to consider the wavelength dependence of photodesorption yields and mechanisms. In this work, for the first time, the wavelength-dependent photodesorption of pure CO ice is explored between 90 and 170 nm. The experiments are performed under ultra high vacuum conditions using tunable synchrotron radiation. Ice photodesorption is simultaneously probed by infrared absorption spectroscopy in reflection mode of the ice and by quadrupole mass spectrometry of the gas phase. The experimental results for CO reveal a strong wavelength dependence directly linked to the vibronic transition strengths of CO ice, implying that photodesorption is induced by electronic transition (DIET). The observed dependence on the ice absorption spectra implies relatively low photodesorption yields at 121.6 nm (Ly alpha), where CO barely absorbs, compared to the high yields found at wavelengths coinciding with transitions into the first electronic state of CO (A(1)Pi at 150 nm); the CO photodesorption rates depend strongly on the UV profiles encountered in different star formation environments.