The physical characterization of carbonate‐bearing normal faults is fundamental for resource development and seismic hazard. Here we report laboratory measurements of density, porosity, Vp, Vs, elastic moduli, and permeability for a range of effective confining pressures (0.1–100 MPa), conducted on samples representing different structural domains of a carbonate‐bearing fault. We find a reduction in porosity from the fault breccia (11.7% total and 6.2% connected) to the main fault plane (9% total and 3.5% connected), with both domains showing higher porosity compared to the protolith (6.8% total and 1.1% connected). With increasing confining pressure, P wave velocity evolves from 4.5 to 5.9 km/s in the fault breccia, is constant at 5.9 km/s approaching the fault plane and is low (4.9 km/s) in clay‐rich fault domains. We find that while the fault breccia shows pressure sensitive behavior (a reduction in permeability from 2 × 10−16 to 2 × 10−17 m2), the cemented cataclasite close to the fault plane is characterized by pressure‐independent behavior (permeability 4 × 10−17 m2). Our results indicate that the deformation processes occurring within the different fault structural domains influence the physical and transport properties of the fault zone. In situ Vp profiles match well the laboratory measurements demonstrating that laboratory data are valuable for implications at larger scale. Combining the experimental values of elastic moduli and frictional properties it results that at shallow crustal levels, M ≤ 1 earthquakes are less favored, in agreement with earthquake‐depth distribution during the L'Aquila 2009 seismic sequence that occurred on carbonates.