Wounded leaves communicate their damage status to one another through a poorly understood process of long-distance signalling. This stimulates the distal production of jasmonates, potent regulators of defence responses. Using non-invasive electrodes we mapped surface potential changes in Arabidopsis thaliana after wounding leaf eight and found that membrane depolarizations correlated with jasmonate signalling domains in undamaged leaves. Furthermore, current injection elicited jasmonoyl-isoleucine accumulation, resulting in a transcriptome enriched in RNAs encoding key jasmonate signalling regulators. From among 34 screened membrane protein mutant lines, mutations in several clade 3 GLUTAMATE RECEPTOR-LIKE genes (GLRs 3.2, 3.3 and 3.6) attenuated wound-induced surface potential changes. Jasmonate-response gene expression in leaves distal to wounds was reduced in a glr3.3 glr3.6 double mutant. This work provides a genetic basis for investigating mechanisms of long-distance wound signalling in plants and indicates that plant genes related to those important for synaptic activity in animals function in organ-to-organ wound signalling.