We present the first search for dark matter-induced delayed coincidence signals in a dual-phase xenon time projection chamber, using the 224.6 live days of the XENON100 science run II. This very distinct signature is predicted in the framework of magnetic inelastic dark matter which has been proposed to reconcile the modulation signal reported by the DAMA/LIBRA collaboration with the null results from other direct detection experiments. No candidate event has been found in the region of interest and upper limits on the WIMPs magnetic dipole moment are derived. The scenarios proposed to explain the DAMA/LIBRA modulation signal by magnetic inelastic dark matter interactions of WIMPs with masses of 58.0 GeV/c$^2$ and 122.7 GeV/c$^2$ are excluded at 3.3 $sigma$ and 9.3 $sigma$, respectively.
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