Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid-solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field HH. At the transition field HsHs, the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length ξ∝|H2−H2s|−1/2ξ∝|H2−Hs2|−1/2. Mean-field critical exponents are predicted, since the upper critical dimension of the transition is du=2du=2. Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.