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The high-resolution (R=25,000) infrared M-band spectrum of the massive protostar NGC 7538 IRS 9 shows a narrow absorption feature at 4.779 µm (2092.3 cm^–1) that we attribute to the vibrational stretching mode of the ¹³CO isotope in pure CO icy grain mantles. This is the first detection of ¹³CO in icy grain mantles in the interstellar medium. The ¹³CO band is a factor of 2.3 narrower than the apolar component of the ¹²CO band. With this in mind, we discuss the mechanisms that broaden solid-state absorption bands. It is shown that ellipsoidally shaped pure CO grains fit the bands of both isotopes at the same time. Slightly worse but still reasonable fits are also obtained by CO embedded in N₂-rich ices and thermally processed O₂-rich ices. In addition, we report new insights into the nature and evolution of interstellar CO ices by comparing the very high resolution multicomponent solid ¹²CO spectrum of NGC 7538 IRS 9 with that of the previously studied low-mass source L1489 IRS. The narrow absorption of apolar CO ices is present in both spectra but much stronger in NGC 7538 IRS 9. It is superposed on a smooth broad absorption feature well fitted by a combination of CO₂and H₂O-rich laboratory CO ices. The abundances of the latter two ices, scaled to the total H₂O ice column, are the same in both sources. We thus suggest that thermal processing manifests itself as evaporation of apolar ices only and not the formation of CO₂or polar ices. Finally, the decomposition of the ¹²CO band is used to derive the ¹²CO/¹³CO abundance ratio in apolar ices. A ratio of ¹²CO/¹³CO=71±15 (3 σ) is deduced, in good agreement with gas-phase CO studies (∼77) and the solid ¹²CO₂/¹³CO₂ratio of 80±11 found in the same line of sight. The implications for the chemical path along which CO₂is formed are discussed.