Abstract We show that the explosion of the first supernovae can trigger low-mass star formation via gravitational fragmentation of the supernova-driven gas shell. If the shell mass does not exceed the host galaxy gas mass, all explosions with energies E SN⩾10 51 erg can lead to shell fragmentation. However, the minimum ambient density required to induce such fragmentation is much larger, n 0>300 cm −3, for Type II supernovae than for pair-instability ones, which can induce star formation even at lower ambient densities. The typical mass of the unstable fragments is ∼10 4−7 M ⊙; their density is in the range 110–6×10 7 cm −3. Fragments have a metallicity strictly lower than 10 −2.6 Z ⊙ and large values of the gravitational-to-pressure force ratio f≃8. Based on these findings, we conclude that the second generation of stars produced by such self-propagating star formation is predominantly constituted by low-mass, long-living, extremely metal-poor (or even metal-free, if mixing is suppressed) stars. We discuss the implications of such results for Pop III star formation scenarios and for the most iron-poor halo star HE0107-5240.