The distribution of permeability in the upper oceanic crust controls hydrothermal circulation and the water–rock interactions that feed seafloor mineralization. A prevailing view is that lavas behave as fractured aquifers whose permeability is dominated by major extensional faults flanked by damage zones. Comparatively little is known about the permeability of the km-wide blocks of crust that lie between major faults, yet such blocks constitute huge sources of leachable metals. Our field mapping of hydrothermal veins and pervasive alteration in spreading-axis lavas in the Semail ophiolite enables quantification of the permeability of distal blocks. Fracture length intensities are only ~0.005 m per m2 of outcrop, an order of magnitude lower than in major fault zones. Laboratory measurements show the rock-matrix permeability of lava outcrops is ~2.5 x 10−16 m2. Numerical hydraulic simulations using dfnWorks software yield bulk permeability of ~5 x 10−16 m2 when flow through the fracture network and the rock-matrix are coupled. This demonstrates that the rock-matrix is as permeable as the sparse and unconnected fracture network, consistent with the thoroughly pervasive, rather than fracture-controlled, nature of greenschist-facies hydrothermal alteration observed in the distal Semail lavas. Our observations and calculated bulk permeabilities provide an updated view of fluid flow through the upper crust, in which matrix-flow controls circulation through large blocks of lavas, enhanced by fault-damage zones at km-scale intervals. This new perspective explains how the rock matrix in oceanic lavas is accessible for leaching of metals for seafloor sulphide deposits.