Recurrent missense mutations in the RNA polymerase II Mediator subunit MED12 are associated with X-linked intellectual disability (XLID) and multiple congenital anomalies, including craniofacial, musculoskeletal, and behavioral defects in humans with FG (or Opitz-Kaveggia) and Lujan syndromes. However, the molecular mechanism(s) underlying these phenotypes is poorly understood. Here we report that MED12 mutations R961W and N1007S causing FG and Lujan syndromes, respectively, disrupt a Mediator-imposed constraint on GLI3-dependent Sonic Hedgehog (SHH) signaling. We show that the FG/R961W and Lujan/N1007S mutations disrupt the gene-specific association of MED12 with a second Mediator subunit, CDK8, identified herein to be a suppressor of GLI3 transactivation activity. In FG/R961W and Lujan/N1007S patient-derived cells, we document enhanced SHH pathway activation and GLI3-target gene induction coincident with impaired recruitment of CDK8 onto promoters of GLI3-target genes, but not non-GLI3-target genes. Together, these findings suggest that dysregulated GLI3-dependent SHH signaling contributes to phenotypes of individuals with FG and Lujan syndromes and further reveal a basis for the gene-specific manifestation of pathogenic mutations in a global transcriptional coregulator.