Heavy-ion collisions at small beam energies have the potential to reveal the rich phase structure of QCD at low temperature and nonzero density. In this case spatially modulated regimes with a "moat" spectrum can arise, where the minimum of the energy is over a sphere at nonzero momentum. We show that if the matter created in heavy-ion collisions freezes out in such a regime, particle numbers and their correlations peak at nonzero, instead of zero, momentum. This effect is much more dramatic for multiparticle correlations than for single-particle spectra. Our results can serve as a first guideline for a systematic search of spatially modulated phases in heavy-ion collisions.