Melt inclusions are used to study the origin and evolution of magmas. The extent to which they represent equilibrium melt compositions, however, critically hinges on the ratio of crystal growth rate to diffusion rate in melts. If the rate of crystal growth is limited by the supply of nutrients and the dissipation of unwanted components, the trapped melt will be depleted in compatible elements and enriched in incompatible elements. Despite widespread recognition of the potential for melt inclusions to trap disequilibrium compositions, their identification remains a challenge. Here, we demonstrate how stable isotopes provide a solution to this problem. Melt inclusions in basaltic tephra from Kīlauea volcano, Hawai‘i, display Mg isotope fractionation up to 0.49‰ (²⁶Mg/²⁴Mg) relative to bulk rock. These observations indicate that kinetic processes, such as chemical diffusion, are at play, as equilibrium mineral-melt isotope fractionation at high temperatures is an order of magnitude smaller. We propose that the heavy Mg isotopic compositions of the melt inclusions were generated by the faster diffusion and thus preferential incorporation of ²⁴Mg by the growing olivine, leaving the slower diffusant (²⁶Mg) behind. The incompatible elements (e.g., Ca, Ti, and K) are predicted to display similarly large fractionations when boundary layer effects are significant. These findings show that stable isotopes can be a useful tool in identifying disequilibrium compositions in melt inclusions.