Continental rifts begin and develop through repeated episodes of faulting and magmatism, but strain partitioning between faulting and magmatism during discrete rifting episodes remains poorly documented. In highly evolved rifts, tensile stresses from far-field plate motions accumulate over decades before being released during relatively short time intervals by faulting and magmatic intrusions. These rifting crises are rarely observed in thick lithosphere during the initial stages of rifting. Here we show that most of the strain during the July-August 2007 seismic crisis in the weakly extended Natron rift, Tanzania, was released aseismically. Deformation was achieved by slow slip on a normal fault that promoted subsequent dyke intrusion by stress unclamping. This event provides compelling evidence for strain accommodation by magma intrusion, in addition to slip along normal faults, during the initial stages of continental rifting and before significant crustal thinning.