NASA sent the Double Asteroid Redirection Test (DART) mission to impact Dimorphos, the satellite of the asteroid binary system (65803) Didymos. DART will release LICIACube prior to impact to obtain high-resolution post-impact images. The impact will produce a crater and a large amount of material ejected at high speed (several tens of m s−1), producing an ejecta cone that will quickly disperse. We analysed an additional effect: the lofting of material at low velocity due to the generation of seismic waves that propagate inside Dimorphos, producing surface shaking far from the impact point. We divide the process into different stages: from the generation of impact-induced waves, the interaction of them with surface particles, the ejection of dust particles at velocities, and the prediction of the observability of the dust coma and trail. We anticipate the following observable effects: (i) generation of a dust cloud that will produce a hazy appearance of Dimorphos’ surface, detectable by LICIACube; (ii) brightness increase of the binary system due to enhancement of the cross-section produced by the dust cloud; (iii) generation of a dust trail, similar to those observed in some Active Asteroids, which can last for several weeks after impact. Numerical prediction of the detectability of these effects depends on the amount and size distribution of ejected particles, which are largely unknown. In case these effects are observable, an inversion method can be applied to compute the amount of ejected material and its velocity distribution, and discuss the relevance of the shaking process.