Fragmentation of porous magma that is subject to gas overpressure is considered to be a crucial process in the generation of explosive volcanic eruptions. A decompressive event (e.g., rapid magma ascent, landslide, dome collapse) disrupts the stress equilibrium between the gas phase and the surrounding melt. When the gas in the pores is exposed to a pressure gradient, it may either fragment the surrounding magma or escape from the magma along an existing pathway of cracks and interconnected bubbles. Therefore, magma permeability can be a decisive parameter in determining if an eruption experiences fragmentation (i.e., whether it is explosive or effusive, or exhibits a temporal transition between the two eruptive styles). Despite the central role that gas permeability may play in the fragmentation of volcanic rocks, previous studies have not experimentally verified or quantified this influence. Based on a comprehensive database of combined permeability and fragmentation experiments, we show that high permeability substantially increases the overpressure required to fragment porous volcanic rocks. Our results allow us to deduce a fragmentation criterion that incorporates gas permeability as well as porosity and internal overpressure. This criterion implies that the energy required for fragmentation is less dependent on the actual pore geometry than on the way the void space is interconnected and, thus, on the contribution of permeable gas flow to decompression.