Aims. In the framework of the GAPS project, we observed the planet-hosting star KELT-9 (A-type star, v sin i ~ 110 km s⁻¹) with the HARPS-N spectrograph at the Telescopio Nazionale Galileo. In this work we analyse the spectra and the extracted radial velocities to constrain the physical parameters of the system and to detect the planetary atmosphere of KELT-9b. Methods. We extracted the mean stellar line profiles from the high-resolution optical spectra via an analysis based on the least-squares deconvolution technique. Then we computed the stellar radial velocities with a method optimised for fast rotators by fitting the mean stellar line profile with a purely rotational profile instead of using a Gaussian function. Results. The new spectra and analysis led us to update the orbital and physical parameters of the system, improving in particular the value of the planetary mass to M_p = 2.88 ± 0.35 M_Jup. We discovered an anomalous in-transit radial velocity deviation from the theoretical Rossiter-McLaughlin effect solution, calculated from the projected spin-orbit angle λ = −85.78 ± 0.46 degrees measured with Doppler tomography. We prove that this deviation is caused by the planetary atmosphere of KELT-9b, thus we call this effect Atmospheric Rossiter-McLaughlin effect. By analysing the magnitude of the radial velocity anomaly, we obtained information on the extension of the planetary atmosphere as weighted by the model used to retrieve the stellar mean line profiles, which is up to 1.22 ± 0.02 R_p. Conclusions. The Atmospheric Rossiter-McLaughlin effect will be observable for other exoplanets whose atmosphere has non-negligible correlation with the stellar mask used to retrieve the radial velocities, in particular ultra-hot Jupiters with iron in their atmospheres. The duration and amplitude of the effect will depend not only on the extension of the atmosphere, but also on the in-transit planetary radial velocities and on the projected rotational velocity of the parent star.