Engineering light-sensitive protein regulators has been a tremendous multidisciplinary challenge. Optogenetic regulators of MAPKs, central nodes of cellular regulation, have not previously been described. Here we present OptoJNKi, a light-regulated JNK inhibitor based on the AsLOV2 light-sensor domain using the ubiquitous FMN chromophore. OptoJNKi gene-transfer allows optogenetic applications, whereas protein delivery allows optopharmacology. Development of OptoJNKi suggests a design principle for other optically regulated inhibitors. From this, we generate Optop38i, which inhibits p38MAPK in intact illuminated cells. Neurons are known for interpreting temporally-encoded inputs via interplay between ion channels, membrane potential and intracellular calcium. However, the consequences of temporal variation of JNK-regulating trophic inputs, potentially resulting from synaptic activity and reversible cellular protrusions, on downstream targets are unknown. Using OptoJNKi, we reveal maximal regulation of c-Jun transactivation can occur at unexpectedly slow periodicities of inhibition depending on the inhibitor's subcellular location. This provides evidence for resonance in metazoan JNK-signalling circuits.