In this paper we discuss variational message passing-based (VMP) inference in a switching Hierarchical Gaussian Filter (HGF). An HGF is a flexible hierarchical state space model that supports closed-form VMP-based approximate inference for tracking of both states and slowly time-varying parameters. Since natural signals often submit to regime-switching dynamics, there is a need for low-complexity closed-form inference in switching state space models. Here we extend the HGF model with parameter switching mechanics and derive closed-form VMP update rules for plug-in applications in factor graph-based models. These VMP rules support both tracking of latent variables and variational free energy as a model performance measure. We show that the switching HGF performs better than a non-switching HGF on modelling of a stock market data set.