The recent development of circuit quantum electrodynamics has brought the possibility to study the interactions between light and circuits of arbitrary complexity on chip. Here, we demonstrate a hybrid architecture using single wall carbon nanotube based quantum dot (QD) inserted in a superconducting microwave cavity. At low temperature, this QD behaves as a tunable artificial atom where the Kondo effect is observable. Simultaneously to the low frequency transport spectroscopy, we study the response of the microwave cavity when the dot is in the Kondo regime. This allows us to probe dynamical aspects of the Kondo effect which are inaccessible to conventional transport measurements.