The lateral flow of magma and ductile deformation of the lower crust along oceanic spreading axes has been thought to play a significant role in suppressing both mid-ocean ridge segmentation and variations in crustal thickness. Direct investigation of such flow patterns is hampered by the kilometres of water that cover the oceanic crust, but such studies can be made on ophiolites (fragments of oceanic crust accreted to a continent). In the Oman ophiolite, small-scale radial patterns of flow have been mapped along what is thought to be the relict of a fast-spreading mid-ocean ridge. Here we present evidence for broad-scale along-axis flow that has been frozen into the gabbro of the Troodos ophiolite in Cyprus (thought to be representative of a slow-spreading ridge axis). The gabbro suite of Troodos spans nearly 20 km of a segment of a fossil spreading axis, near a ridge-transform intersection. We mapped the pattern of magma flow by analysing the rocks' magnetic fabric at 20 sites widely distributed in the gabbro suite, and by examining the petrographic fabric at 9 sites. We infer an along-axis magma flow for much of the gabbro suite, which indicates that redistribution of melt occurred towards the segment edge in a large depth range of the oceanic crust. Our results support the magma plumbing structure that has been inferred indirectly from a seismic tomography experiment on the slow-spreading Mid-Atlantic Ridge.