Graphene is inherently sensitive to vicinal dielectrics and local charge distributions, a property that can be probed by the position of the Dirac point in graphene field‐effect transistors. Exploiting this as a useful sensing principle requires selectivity; however, graphene itself exhibits no molecule‐specific interaction. Complementarily, metal–organic frameworks can be tailored to selective adsorption of specific molecular species. Here, a selective ethanol sensor is demonstrated by growing a surface‐mounted metal–organic framework (SURMOF) directly onto graphene field‐effect transistors (GFETs). Unprecedented shifts of the Dirac point, as large as 15 V, are observed when the SURMOF/GFET is exposed to ethanol, while a vanishingly small response is observed for isopropanol, methanol, and other constituents of the air, including water. The synthesis and conditioning of the hybrid materials sensor with its functional characteristics are described and a model is proposed to explain the origin, magnitude, and direction of the Dirac point voltage shift. Tailoring multiple SURMOFs to adsorb specific gases on an array of such devices thus generates a versatile, selective, and highly sensitive platform for sensing applications.