Marine heatwaves (MHWs)-discrete but prolonged periods of anomalously warm ocean temperatures-can drastically alter ocean ecosystems, with profound ecological and socioeconomic impacts(1-8). Considerable effort has been directed at understanding the patterns, drivers and trends of MHWs globally(9-11). Typically, MHWs are characterized on the basis of their intensity and persistence at a given location-an approach that is particularly relevant for corals and other sessile organisms that must endure increased temperatures. However, many ecologically and commercially important marine species respond to environmental disruptions by relocating to favourable habitats, and dramatic range shifts of mobile marine species are among the conspicuous impacts of MHWs(1,4,12,13). Whereas spatial temperature shifts have been studied extensively in the context of long-term warming trends(14-18), they are unaccounted for in existing global MHW analyses. Here we introduce thermal displacement as a metric that characterizes MHWs by the spatial shifts of surface temperature contours, instead of by local temperature anomalies, and use an observation-based global sea surface temperature dataset to calculate thermal displacements for all MHWs from 1982 to 2019. We show that thermal displacements during MHWs vary from tens to thousands of kilometres across the world's oceans and do not correlate spatially with MHW intensity. Furthermore, short-term thermal displacements during MHWs are of comparable magnitude to century-scale shifts inferred from warming trends(18), although their global spatial patterns are very different. These results expand our understanding of MHWs and their potential impacts on marine species, revealing which regions are most susceptible to thermal displacement, and how such shifts may change under projected ocean warming. The findings also highlight the need for marine resource management to account for MHW-driven spatial shifts, which are of comparable scale to those associated with long-term climate change and are already happening. Ocean heatwaves displace surface isotherms by tens to thousands of kilometres-comparable to shifts associated with long-term warming trends-potentially driving rapid redistributions of marine species.