We develop a theory of interaction of a classical plasma with Kaluza-Klein (KK) gravitons in the ADD model of TeV-scale gravity. The plasma is described in the kinetic approach as a system of charged particles and the Maxwell field, both confined to the brane. Interaction with multidimensional gravity living in the bulk with n compact extra dimensions is introduced within a linearized theory. The KK graviton emission rates are computed taking into account plasma collective effects through two-point correlation functions of fluctuations of the plasma energy-momentum tensor. Apart from known mechanisms (such as bremsstrahlung and the gravi-Primakoff effect), we find essentially collective channels such as coalescence of plasma waves into gravitons which may be manifest in turbulent plasmas. Our results indicate that the commonly used KK gravitons production rates in stars and supernovae may be underestimated.