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Abstract Atmospheric convectively coupled equatorial Kelvin waves (CCKWs) are a major tropical weather feature strongly influenced by ocean–atmosphere interactions. However, prediction of the development and propagation of CCKWs remains a challenge for models. The physical processes involved in these interactions are assessed by investigating the oceanic response to the passage of CCKWs across the eastern Indian Ocean and Maritime Continent using the NEMO ocean model analysis with data assimilation. Three‐dimensional life cycles are constructed for “solitary” CCKW events. As a CCKW propagates over the eastern Indian Ocean, the immediate thermodynamic ocean response includes cooling of the ocean surface and subsurface, deepening of the mixed layer depth, and an increase in the mixed layer heat content. Additionally, a dynamical downwelling signal is observed two days after the peak in the CCKW westerly wind burst, which propagates eastward along the Equator and then follows the Sumatra and Java coasts, consistent with a downwelling oceanic Kelvin wave with an average phase speed of 2.3 m s⁻¹. Meridional and vertical structures of zonal velocity anomalies are consistent with this framework. This dynamical feature is consistent across distinct CCKW populations, indicating the importance of CCKWs as a source of oceanic Kelvin waves in the eastern Indian Ocean. The subsurface dynamical response to the CCKWs is identifiable up to 11 days after the forcing. These ocean feedbacks on time scales longer than the CCKW life cycle help elucidate how locally driven processes can rectify onto longer time‐scale processes in the coupled ocean–atmosphere system.