Axions are a viable candidate for cold dark matter, which should generically form minihalos of subplanetary masses from white-noise isocurvature density fluctuations if the Peccei-Quinn phase transition occurs after inflation. Despite being denser than the larger halos formed out of adiabatic fluctuations from inflation, axion minihalos have surface densities much smaller than the critical value required for gravitational lensing to produce multiple images or high magnification, and hence are practically undetectable as lenses in isolation. However, their lensing effect can be enhanced when superposed near critical curves of other lenses. We propose a method to detect them through photometric monitoring of recently discovered caustic transiting stars behind cluster lenses, under extreme magnification factors 103-104 as the lensed stars cross microlensing caustics induced by intracluster stars. For masses of the first gravitationally collapsed minihalos in the range ∼10−15-10−8 h−1 M , we show that axion minihalos in galaxy clusters should collectively produce subtle surface density fluctuations of amplitude ∼10−4-10−3 on projected length scales of ∼10-104 au, which imprint irregularities on the microlensing lightcurves of caustic transiting stars. We estimate that, inside a cluster halo and over the age of the universe, most of these minihalos are likely to avoid dynamic disruption by encounters with stars or other minihalos.