Marine heatwaves (MHWs), episodic periods of abnormally high sea surface temperature, severely affect marine ecosystems. Large marine ecosystems (LMEs) cover ~22% of the global ocean but account for 95% of global fisheries catches. Yet how climate change affects MHWs over LMEs remains unknown because such LMEs are confined to the coast where low-resolution climate models are known to have biases. Here, using a high-resolution Earth system model and applying a ‘future threshold’ that considers MHWs as anomalous warming above the long-term mean warming of sea surface temperatures, we find that future intensity and annual days of MHWs over the majority of the LMEs remain higher than in the present-day climate. Better resolution of ocean mesoscale eddies enables simulation of more realistic MHWs than low-resolution models. These increases in MHWs under global warming pose a serious threat to LMEs, even if resident organisms could adapt fully to the long-term mean warming.