The connectivity of rocks’ porous structure and the presence of fractures influence the transfer of fluids in the Earth’s crust. Here, we employed laboratory experiments to measure the influence of macro-fractures and effective pressure on the permeability of volcanic rocks with a wide range of initial porosities (1–41 vol. %) comprised of both vesicles and micro-cracks. We used a hand-held permeameter and hydrostatic cell to measure the permeability of intact rock cores at effective pressures up to 30 MPa; we then induced a macro-fracture to each sample using Brazilian tensile tests and measured the permeability of these macro-fractured rocks again. We show that intact rock permeability increases non-linearly with increasing porosity and decreases with increasing effective pressure due to compactional closure of micro-fractures. Imparting a macro-fracture both increases the permeability of rocks and their sensitivity to effective pressure. The magnitude of permeability increase induced by the macro-fracture is more significant for dense rocks. We finally provide a general equation to estimate the permeability of intact and fractured rocks, forming a basis to constrain fluid flow in volcanic and geothermal systems.