Two-neutrino double electron capture is a rare nuclear decay where two electrons are simultaneously captured from the atomic shell. For Xe124 this process has not yet been observed and its detection would provide a new reference for nuclear matrix element calculations. We have conducted a search for two-neutrino double electron capture from the K shell of Xe124 using 7636 kgd of data from the XENON100 dark matter detector. Using a Bayesian analysis we observed no significant excess above background, leading to a lower 90% credibility limit on the half-life T1/2>6.5×1020 yr. We have also evaluated the sensitivity of the XENON1T experiment, which is currently being commissioned, and found a sensitivity of T1/2>6.1×1022 yr after an exposure of 2 tyr.