The Down syndrome-associated DYRK1A kinase has been reported as a stimulator of the developmentally important Hedgehog (Hh) pathway, but cells from Down syndrome patients paradoxically display reduced Hh signalling activity. Here we find that DYRK1A stimulates GLI transcription factor activity through phosphorylation of general nuclear localization clusters. In contrast, in vivo and in vitro experiments reveal that DYRK1A kinase can also function as an inhibitor of endogenous Hh signalling by negatively regulating ABLIM proteins, the actin cytoskeleton and the transcriptional co-activator MKL1 (MAL). As a final effector of the DYRK1A-ABLIM-actin-MKL1 sequence, we identify the MKL1 interactor Jumonji domain demethylase 1A (JMJD1A) as a novel Hh pathway component stabilizing the GLI1 protein in a demethylase-independent manner. Furthermore, a Jumonji-specific small-molecule antagonist represents a novel and powerful inhibitor of Hh signal transduction by inducing GLI1 protein degradation in vitro and in vivo.