Low-earth-orbit (LEO) satellite communication systems that use millimeter-wave frequencies rely on large antenna arrays with hybrid analog-digital architectures for rapid beam steering. LEO satellites are only visible from the ground for short periods of times (a few tens of minutes) due to their high orbital speeds. This paper presents a variational message passing algorithm for joint localization and beam tracking of a LEO satellite from a ground station equipped with a hybrid transceiver architecture. The algorithm relies on estimating the parameters of the orbit, which is modelled as circular. Angles are then obtained from the orbit in a straightforward manner. Simulation results show that the proposed method is highly resilient to missed detections, enables reliable satellite tracking even near the horizon, and effectively alleviates the ambiguities inherent in hybrid architectures.