Many compelling models predict dark matter coupling to the electromagnetic current through higher multipole interactions, while remaining electrically neutral. Different multipole couplings have been studied, among them anapole moment, electric and magnetic dipole moments, and millicharge. This study sets limits on the couplings for these photon-mediated interactions using nonrelativistic contact operators in an effective field theory framework. Using data from the PICO-60 bubble chamber leading limits for dark matter masses between 2.7 GeV/c 2 and 24 GeV/c 2 are reported for the coupling of these photon-mediated dark matter-nucleus interactions. The detector was filled with 52 kg of C3F8 operating at thermodynamic thresholds of 2.45 keV and 3.29 keV, reaching exposures of 1404 kg-day and 1167 kg-day, respectively.