An implantable pressure sensor, which may be incorporated within an implantable medical electrical lead, includes an insulative sidewall, which contains a gap capacitor and an integrated circuit. The insulative sidewall of the pressure sensor includes a pressure sensitive diaphragm portion, and the gap capacitor includes a first electrode plate, which is attached to an interior surface of the diaphragm portion of the sidewall, and a second electrode plate, which is spaced apart from the first electrode plate and coupled to the integrated circuit, which is coupled, through the sidewall, to a supply contact and a ground contact. A conductive layer extends over one of the interior surface of the diaphragm portion of the sidewall and an exterior surface of the diaphragm portion; and the conductive layer is coupled to the ground contact to either shield or ground the first electrode plate.